On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and cont...On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].展开更多
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
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
Characterization theorems for abundant sernigroups having a quasi-ideal quasi-adequate transversal are obtained. Our results generalize and amplify the related results of Satio on regular semigroup obtained in 1985 an...Characterization theorems for abundant sernigroups having a quasi-ideal quasi-adequate transversal are obtained. Our results generalize and amplify the related results of Satio on regular semigroup obtained in 1985 and Kong obtained in 2007 respectively. Some recent results on this topic given by Guo-Shum are strengthened. In particular, the structure of such an abundant semigroup is described.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 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,we investigate a class of factorisable IC quasi-adequate semigroups,so-called,factorisable IC quasi-adequate semigroups of type-（H,I）.Some characterizations of factorisable IC quasi-adequate semigroups...In this paper,we investigate a class of factorisable IC quasi-adequate semigroups,so-called,factorisable IC quasi-adequate semigroups of type-（H,I）.Some characterizations of factorisable IC quasi-adequate semigroups of type-（H,I） are obtained.In particular,we prove that any IC quasi-adequate semigroup has a factorisable IC quasi-adequate subsemigroups of type-（H,I） and a band of cancellative monoids.展开更多
文摘On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].
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 National Natural Science Foundation of China (Grant No.10571077)Natural Science Foundation of Gansu Province (Grant No.3ZS052-A25-017)
文摘Characterization theorems for abundant sernigroups having a quasi-ideal quasi-adequate transversal are obtained. Our results generalize and amplify the related results of Satio on regular semigroup obtained in 1985 and Kong obtained in 2007 respectively. Some recent results on this topic given by Guo-Shum are strengthened. In particular, the structure of such an abundant semigroup is described.
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 NSF of Jiangxi Province(0511037)
文摘In this paper,we investigate a class of factorisable IC quasi-adequate semigroups,so-called,factorisable IC quasi-adequate semigroups of type-（H,I）.Some characterizations of factorisable IC quasi-adequate semigroups of type-（H,I） are obtained.In particular,we prove that any IC quasi-adequate semigroup has a factorisable IC quasi-adequate subsemigroups of type-（H,I） and a band of cancellative monoids.
