Some Properties Associated with Adequate Transversals

Canadian mathematical bulletin

Xiangjun Kong¹ 

[1] Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, P. R. China

关键词: abundant semigroup;    adequate transversal;    Green's $*$-relations;    quasi-ideal;   

DOI  :  10.4153/CMB-2011-015-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper, another relationship between the quasi-ideal adequate transversals of an abundant semigroup is given. We introduce the concept of a weakly multiplicative adequate transversal and the classic result that an adequate transversal is multiplicative if and only if it is weakly multiplicative and a quasi-ideal is obtained. Also, we give two equivalent conditions for an adequate transversal to be weakly multiplicative. We then consider the case when $I$ and $Lambda$ (defined below) are bands. This is analogous to the inverse transversal if the regularity condition is adjoined.

【 授权许可】

Unknown