That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and...That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.展开更多
A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band.We deal with congruces on a normal orthodox semigroup with an iverse transversal .A structure theorem for such semigrou...A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band.We deal with congruces on a normal orthodox semigroup with an iverse transversal .A structure theorem for such semigroup is obtained.Munn(1966)gave a fundamental inverse semigroup Following Munn's idea ,we give a fundamental normal orthodox semigroup with an inverse transversal.展开更多
Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel nor...Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel normal system; conversely any P-kernel normal system of S（P） can determine a strong P-congruence.展开更多
The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigrou...Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.展开更多
In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and gener...In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.展开更多
The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from...The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.展开更多
The necessary and sufficient conditions for the semidirect products of two monoids to be left strongly π-inverse are determined. Furthemore,the least group congruence on a strongly π-inverse semidirect is dicussed,a...The necessary and sufficient conditions for the semidirect products of two monoids to be left strongly π-inverse are determined. Furthemore,the least group congruence on a strongly π-inverse semidirect is dicussed,and some important isomorphism theorems are accessed.展开更多
[1]Hall T E.Orthodox semigroups.Pacific J Math,1971,39:677-686[2]Howie J M.An Introduction to Semigroup Theory.Now York:Academic Press,1976[3]Fountain J B.Abundant semigroups.Proc Lond Math Soc,1982,44 (3):103-129[4]E...[1]Hall T E.Orthodox semigroups.Pacific J Math,1971,39:677-686[2]Howie J M.An Introduction to Semigroup Theory.Now York:Academic Press,1976[3]Fountain J B.Abundant semigroups.Proc Lond Math Soc,1982,44 (3):103-129[4]El-Qallali A,Fountain J B.Idempotent-connected abundant semigroups.Proc Roy Soc Edinburgh,1981,Sec.A:79-90[5]El-Qallali A,Fountain J B.Quasi-adequate semigroups.Proc Roy Soc Edinburgh,1981,Sec.A:91-99[6]Fountain J B.Adequate semigroups.Proc Edinburgh Math Soc,1979,22:113-125[7]Guo X J.Abundant C-lpp proper semigroups.Southeast Asian Bull Math,2000,24 (1):41-50[8]Guo X J,Shum K P,Guo Y Q.Perfect rpp semigroups.Communications in Algebra,2001,29(6):2447-2459[9]Ren X M,Shum K P.Structure theorems for right pp-semigroups with left central idempotents.Discussions Math General Algebra and Applications,2000,20:63-75[10]Ren X M,Shum K P.The structure of superabundant semigroups.Sci China Ser A-Math,2004,47(5):756-771[11]Shum K P,Ren X M.Abundant semigroups with left central idempotents.Pure Math Appl,1999,10(1):109-113[12]Armstrong S.The structure of type A semigroups.Semigroup Forum,1984,29:319-336[13]Lawson M V.The structure of type A semigroups.Quart J Math Oxford,1986,37(2):279-298[14]Bailes G L.Right inverse semigroups.J Algebra,1973,26:492-507[15]Venkatesan P S.Right (left) inverse semigroups.J Algebra,1974,31:209-217[16]Yamada M.Orthodox semigroups whose idempotents satisfy a certain identity.Semigroup Forum,1973,6:113-128[17]Preston G B.Semiproducts of semigroups.Proc Roy Soc Edinburgh,1986,102A:91-102[18]Preston G B:Products of semigroups.In:Shum K P,Yuen P C,eds.Proc.of the conference"Ordered structures and algebra of computer languages",1991 (Hong Kong).Singapore:World Scientific Inc,1993.161-169[19]Lawson M V.The natural partial order on an abundant semigroup.Proc Edinburgh Math Soc,1987,30:169-186[20]El-Qallali A.(L)*-unipotent semigroups.J Pure and Applied Algebra,1989。展开更多
It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular...It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.展开更多
We discuss some fundamental properties of inverse semigroups of matrices,and prove that the idempotents of such a semigroup constitute & subsemilattice of a finite Boolean lattice, and that the inverse semigroups ...We discuss some fundamental properties of inverse semigroups of matrices,and prove that the idempotents of such a semigroup constitute & subsemilattice of a finite Boolean lattice, and that the inverse semigroups of some matrices with the same rank are groups.At last,we determine completely the construction of the inverse semigroups of some 2×2 matrices:such a semigroup is isomorphic to a linear group of dimension 2 or a null-adjoined group,or is a finite semilattice of Abelian linear groups of finite dimension,or satisfies some other properties. The necessary and sufficient conditions are given that the sets consisting of some 2×2 matrices become inverse semigroups.展开更多
Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E ｜ arbieary f ∈ E, S（f , e） loheain in w（e）} iso...Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E ｜ arbieary f ∈ E, S（f , e） loheain in w（e）} isomorphic to E° by θ：Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J（E∪ S°） satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J（S°）, called the weakly inverse hull of a weakly inverse system （S°, E, θ, φ） with I（∑） ≌ S°, E（∑） ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given.展开更多
Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-...Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p｜s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.展开更多
文摘That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.
基金Foundation item： Supported by NSF of China（10471112） Supported by Shaanxi Provincial Natural Science Foundation（2005A15） Acknowledgement The authors express their gratitude to the referees for very helpful and detailed comments.
文摘那在那里存在，是众所周知的正统 semigroup 上的最小的反的 semigroup 一致。我们在正统 semigroup 上由 Y 表示最小的反的 semigroup 一致。让 S 是战斗逆 semigroup。我们在 S 上构造部分订单由某种它的 subsemigroups 并且揭开 S 上的部分订单在 S/Y 上与部分订单有靠近的接触。
文摘A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band.We deal with congruces on a normal orthodox semigroup with an iverse transversal .A structure theorem for such semigroup is obtained.Munn(1966)gave a fundamental inverse semigroup Following Munn's idea ,we give a fundamental normal orthodox semigroup with an inverse transversal.
文摘Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel normal system; conversely any P-kernel normal system of S（P） can determine a strong P-congruence.
文摘The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
基金Leading Academic Discipline Project of SHNU,China (No.DZL803)Innovation Project of Shanghai Education Committee,China(No.12YZ081)+2 种基金General Scientific Research Project of SHNU,China (No.SK201121)National Natural Science Foundation of China(No.11001046)Fundamental Research Fundation for the Central Universities,China (No.11D10904)
文摘Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.
文摘In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.
文摘The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.
基金Supported by National Natural Science Foundation of China（90818020） Supported by Scientific Research Foundation of China Jiliang University（20060810）
文摘The necessary and sufficient conditions for the semidirect products of two monoids to be left strongly π-inverse are determined. Furthemore,the least group congruence on a strongly π-inverse semidirect is dicussed,and some important isomorphism theorems are accessed.
文摘[1]Hall T E.Orthodox semigroups.Pacific J Math,1971,39:677-686[2]Howie J M.An Introduction to Semigroup Theory.Now York:Academic Press,1976[3]Fountain J B.Abundant semigroups.Proc Lond Math Soc,1982,44 (3):103-129[4]El-Qallali A,Fountain J B.Idempotent-connected abundant semigroups.Proc Roy Soc Edinburgh,1981,Sec.A:79-90[5]El-Qallali A,Fountain J B.Quasi-adequate semigroups.Proc Roy Soc Edinburgh,1981,Sec.A:91-99[6]Fountain J B.Adequate semigroups.Proc Edinburgh Math Soc,1979,22:113-125[7]Guo X J.Abundant C-lpp proper semigroups.Southeast Asian Bull Math,2000,24 (1):41-50[8]Guo X J,Shum K P,Guo Y Q.Perfect rpp semigroups.Communications in Algebra,2001,29(6):2447-2459[9]Ren X M,Shum K P.Structure theorems for right pp-semigroups with left central idempotents.Discussions Math General Algebra and Applications,2000,20:63-75[10]Ren X M,Shum K P.The structure of superabundant semigroups.Sci China Ser A-Math,2004,47(5):756-771[11]Shum K P,Ren X M.Abundant semigroups with left central idempotents.Pure Math Appl,1999,10(1):109-113[12]Armstrong S.The structure of type A semigroups.Semigroup Forum,1984,29:319-336[13]Lawson M V.The structure of type A semigroups.Quart J Math Oxford,1986,37(2):279-298[14]Bailes G L.Right inverse semigroups.J Algebra,1973,26:492-507[15]Venkatesan P S.Right (left) inverse semigroups.J Algebra,1974,31:209-217[16]Yamada M.Orthodox semigroups whose idempotents satisfy a certain identity.Semigroup Forum,1973,6:113-128[17]Preston G B.Semiproducts of semigroups.Proc Roy Soc Edinburgh,1986,102A:91-102[18]Preston G B:Products of semigroups.In:Shum K P,Yuen P C,eds.Proc.of the conference"Ordered structures and algebra of computer languages",1991 (Hong Kong).Singapore:World Scientific Inc,1993.161-169[19]Lawson M V.The natural partial order on an abundant semigroup.Proc Edinburgh Math Soc,1987,30:169-186[20]El-Qallali A.(L)*-unipotent semigroups.J Pure and Applied Algebra,1989。
基金supported by National Natural Science Foundation of China (Grant No.10571061)
文摘It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.
基金the National Natural Science Foundation of China （No. 10571005）.Acknowledgements The author would like to express his gratitude to Professor Guo Yuqi for his encouragement and guidance, also to all referees for their comments.
文摘We discuss some fundamental properties of inverse semigroups of matrices,and prove that the idempotents of such a semigroup constitute & subsemilattice of a finite Boolean lattice, and that the inverse semigroups of some matrices with the same rank are groups.At last,we determine completely the construction of the inverse semigroups of some 2×2 matrices:such a semigroup is isomorphic to a linear group of dimension 2 or a null-adjoined group,or is a finite semilattice of Abelian linear groups of finite dimension,or satisfies some other properties. The necessary and sufficient conditions are given that the sets consisting of some 2×2 matrices become inverse semigroups.
文摘Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E ｜ arbieary f ∈ E, S（f , e） loheain in w（e）} isomorphic to E° by θ：Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J（E∪ S°） satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J（S°）, called the weakly inverse hull of a weakly inverse system （S°, E, θ, φ） with I（∑） ≌ S°, E（∑） ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given.
文摘Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p｜s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.
