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
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 introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croi...In this paper, we introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croisot＇s Theory of Decomposition for F-semigroups, we introduce and study the absorbent and regular absorbent Г-semigroups. We approach this problem by examining quasi-ideals using Green＇s relations.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.
文摘In this paper, we introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croisot＇s Theory of Decomposition for F-semigroups, we introduce and study the absorbent and regular absorbent Г-semigroups. We approach this problem by examining quasi-ideals using Green＇s relations.
