In this paper, we discuss some properties about an abundant semigroup with a quasi-ideal adequate transversal. Moreover, we show that the product of two quasi-ideal adequate transversals of an abundant semigroup which...In this paper, we discuss some properties about an abundant semigroup with a quasi-ideal adequate transversal. Moreover, we show that the product of two quasi-ideal adequate transversals of an abundant semigroup which satisfies some conditions is a quasiideal adequate transversal.展开更多
In this paper we establish a construction of a class of left E-adequate semigroups by using semilattices of cancellative monoids and fundamental left E-adequate semigroups. We first introduce concepts of type μ^＋（...In this paper we establish a construction of a class of left E-adequate semigroups by using semilattices of cancellative monoids and fundamental left E-adequate semigroups. We first introduce concepts of type μ^＋（μ^＊,μ ） abundant semigroups and type μ^＋left E-adequate semigroups. In fact, regular semigroups are type μ^＋abundant semigroups and inverse semigroups are type μ^＋left E-adequate semigroups. Next, we construct a special kind of algebras called E^＋-product. It is proved that every E^＋-product is a type μ^＋left E-adequate semigroup, and every type μ^＋left E-adequate semigroup is isomorphic to an E^＋-product of a semilattice of cancellative monoids with a fundamental left E-adequate semigroup. Finally, as a corollary of the main result, it is deduced that every inverse semigroup is isomorphic to an E^＋-product of a Clifford semigroup by a fundamental inverse semigroup.展开更多
In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and ...In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.展开更多
The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transver...The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by McAlister and Blyth on split orthodox semigroups.展开更多
In this paper, we first study the structure of quasi-adequate semigroups with a cancellative monoid transversal. By using the above result, we present a method of construction for the abundant semigroups containing a ...In this paper, we first study the structure of quasi-adequate semigroups with a cancellative monoid transversal. By using the above result, we present a method of construction for the abundant semigroups containing a CO-adequate transversal.展开更多
In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are character-ized.Our results generalize and enric...In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are character-ized.Our results generalize and enrich Saito＇s results on quasi-orthodox semigroups with an inverse transversal.展开更多
The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal.Some properties and characterizations for such semigroups are obtained.In particular. we establish the structure o...The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal.Some properties and characterizations for such semigroups are obtained.In particular. we establish the structure of this class of abundant semigroups in terms of left normal bands,right normal braids and adequate semigroups with some simple Compatibility conditions.Finally.we apply this structure to some special cases.展开更多
基金Supported by National Natural Science Foundation of China（90818020） Supported by Scientific Research Foundation of China Jiliang University（20060810）
文摘In this paper, we discuss some properties about an abundant semigroup with a quasi-ideal adequate transversal. Moreover, we show that the product of two quasi-ideal adequate transversals of an abundant semigroup which satisfies some conditions is a quasiideal adequate transversal.
基金The NSF (04JJ40001) of Hunanthe Scientific Research Foundation (05A014) of Hunan Education Department
文摘In this paper we establish a construction of a class of left E-adequate semigroups by using semilattices of cancellative monoids and fundamental left E-adequate semigroups. We first introduce concepts of type μ^＋（μ^＊,μ ） abundant semigroups and type μ^＋left E-adequate semigroups. In fact, regular semigroups are type μ^＋abundant semigroups and inverse semigroups are type μ^＋left E-adequate semigroups. Next, we construct a special kind of algebras called E^＋-product. It is proved that every E^＋-product is a type μ^＋left E-adequate semigroup, and every type μ^＋left E-adequate semigroup is isomorphic to an E^＋-product of a semilattice of cancellative monoids with a fundamental left E-adequate semigroup. Finally, as a corollary of the main result, it is deduced that every inverse semigroup is isomorphic to an E^＋-product of a Clifford semigroup by a fundamental inverse semigroup.
基金Supported by the NNSF of China(10961014)Supported by the NSF of Jiangxi ProvinceSupported by the SF of Education Department of Jiangxi Province(GJJ11388)
文摘In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.
基金Supported by National Natural Science Foundation of China of China(Grant No.10961014)Natural Science Foundation of Jiangxi Provincethe SF of Education Department of Jiangxi Province,China(Grant No.GJJ11388)
文摘The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by McAlister and Blyth on split orthodox semigroups.
基金the Natural Science Foundation of Hunan Province （No. 04JJ40001） the Scientific Research Foundation of Hunan Education Department （No. 05A014）.
文摘In this paper, we first study the structure of quasi-adequate semigroups with a cancellative monoid transversal. By using the above result, we present a method of construction for the abundant semigroups containing a CO-adequate transversal.
基金Supported by the Natural Science Foundation Project of Yunnan Education Department (Grant No.09Y0141)a Ph.D Foundation of Yunnan Normal University
文摘In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are character-ized.Our results generalize and enrich Saito＇s results on quasi-orthodox semigroups with an inverse transversal.
基金supported by the foundation of Yunnan University the Natural Science Foundation of Yunnan Province
文摘The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal.Some properties and characterizations for such semigroups are obtained.In particular. we establish the structure of this class of abundant semigroups in terms of left normal bands,right normal braids and adequate semigroups with some simple Compatibility conditions.Finally.we apply this structure to some special cases.
