The product of quasi-ideal refined generalised quasi-adequate transversals

Open Mathematics

卷:17

Wu Yonghong¹  Kong Xiangjun²  Wang Pei³ 

[1] Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia;

[2] School of Mathematical Sciences and School of Statistics, Qufu Normal University, Qufu, 273165, China;

[3] School of Software Engineering, Qufu Normal University, Qufu, 273165, China;

关键词: abundant semigroup;    product;    rgqa transversal;    quasi-ideal;    20m10;   

DOI  :  10.1515/math-2019-0004

来源: DOAJ

【 摘 要 】

As the real common generalisations of both orthodox transversals and adequate transversals in the abundant case, the concept of refined generalised quasi-adequate transversal, for short, RGQA transversal was introduced by Kong and Wang. In this paper, an interesting characterization for a generalised quasi-adequate transversal to be refined is acquired. It is shown that the product of every two quasi-ideal RGQA transversals of the abundant semigroup S satisfying the regularity condition is a quasi-ideal RGQA transversal of S and that all quasi-ideal RGQA transversals of S compose a rectangular band. The related results concerning adequate transversals are generalised and enriched.

【 授权许可】

Unknown