- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Left quasi-abundant semigroups J. Korean Math. Soc. 2019 Vol. 56, No. 5, 1159-1172 https://doi.org/10.4134/JKMS.j180256Published online September 1, 2019 Zhulin Ji, Xueming Ren, Yanhui Wang Xi'an University of Architecture and Technology; Xi'an University of Architecture and Technology; Shandong University of Science and Technology Abstract : A semigroup $S$ is called a weakly abundant semigroup if its every $\widetilde{\mathcal{L}}$-class and every $\widetilde{\mathcal{R}}$-class contains an idempotent. Our purpose is to study an analogue of orthodox semigroups in the class of weakly abundant semigroups. Such an analogue is called a left quasi-abundant semigroup, which is a weakly abundant semigroup with a left quasi-normal band of idempotents and having the congruence condition (C). To build our main structure theorem for left quasi-abundant semigroups, we first give a sufficient and necessary condition of the idempotent set $E(S)$ of a weakly abundant semigroup $S$ being a left quasi-normal band. And then we construct a left quasi-abundant semigroup in terms of weak spined products. Such a result is a generalisation of that of Guo and Shum for left semi-perfect abundant semigroups. In addition, we consider a type $Q$ semigroup which is a left quasi-abundant semigroup having the PC condition. Keywords : weakly abundant semigroups, weak spined products, left quasi-abundant semigroups, type $Q$ semigroups MSC numbers : 20M10 Full-Text :