This paper defines a kind of quasi-regular semigroups and the so-called E-ideal quasiregular semigroups and gives some of its characteristics and its two special cases (E-left regular quasi-regular semigroups, E-semil...This paper defines a kind of quasi-regular semigroups and the so-called E-ideal quasiregular semigroups and gives some of its characteristics and its two special cases (E-left regular quasi-regular semigroups, E-semilattice quasi-regular semigroups), thus estabishing a structure theorem for it, and as corollaries, obtaining a construction for a left regular band and the known construction for bands (Petrich, 1967).展开更多
In this paper,a sufficient condition is given under which the smash product A#H is a transfinite left.free normalizing extension of an algebra A.Moreover,the result is applied to a skew semigroup ring,a skew group rin...In this paper,a sufficient condition is given under which the smash product A#H is a transfinite left.free normalizing extension of an algebra A.Moreover,the result is applied to a skew semigroup ring,a skew group ring and the quantum group U_q(sl(2))such that some properties are shown.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
The aim of this paper is to study a class of right pp semigroups, so-called pseudo-C- rpp semigroups. After obtaining some characterizations of pseudo-C-rpp semigroups, we establish a construction of such semigroups i...The aim of this paper is to study a class of right pp semigroups, so-called pseudo-C- rpp semigroups. After obtaining some characterizations of pseudo-C-rpp semigroups, we establish a construction of such semigroups in terms of left normal bands and right C-rpp semigroups. In particular, a special case is considered.展开更多
In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups ...In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups play an essential role in studying the structure,especially the decomposition,of semigroups.The purpose of this paper is to deal with the algebraic structure of semigroups by applying picture fuzzy set theory.As an application of our results we get characterisations of intra-regular regular semigroups in terms of picture fuzzy bi-ideals.We prove that a semigroup is both regular and intra-regular if and only if every picture fuzzy bi-ideal on S is idempotent.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘This paper defines a kind of quasi-regular semigroups and the so-called E-ideal quasiregular semigroups and gives some of its characteristics and its two special cases (E-left regular quasi-regular semigroups, E-semilattice quasi-regular semigroups), thus estabishing a structure theorem for it, and as corollaries, obtaining a construction for a left regular band and the known construction for bands (Petrich, 1967).
基金Project (19501007) supported by the National Natural Science Foundation of China
文摘In this paper,a sufficient condition is given under which the smash product A#H is a transfinite left.free normalizing extension of an algebra A.Moreover,the result is applied to a skew semigroup ring,a skew group ring and the quantum group U_q(sl(2))such that some properties are shown.
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.
基金Supported by the NSF of Jiangxi Provincethe SF of Education Department of Jiangxi Provincethe SF of Jiangxi Normal University
文摘The aim of this paper is to study a class of right pp semigroups, so-called pseudo-C- rpp semigroups. After obtaining some characterizations of pseudo-C-rpp semigroups, we establish a construction of such semigroups in terms of left normal bands and right C-rpp semigroups. In particular, a special case is considered.
文摘In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups play an essential role in studying the structure,especially the decomposition,of semigroups.The purpose of this paper is to deal with the algebraic structure of semigroups by applying picture fuzzy set theory.As an application of our results we get characterisations of intra-regular regular semigroups in terms of picture fuzzy bi-ideals.We prove that a semigroup is both regular and intra-regular if and only if every picture fuzzy bi-ideal on S is idempotent.
