Affiliations: [a] School of Science, East China JiaotongUniversity, Nanchang, Jiangxi, China
| [b] School of Mathematics & Computer Science, Guizhou Normal University, Guiyang, Guizhou, China
Correspondence:
[*]
Corresponding author. Chunhua Li, School of Science, East China Jiaotong University, Nanchang, Jiangxi 330013, China. E-mail: [email protected].
Abstract: In this paper, the notion of a fuzzy *–ideal of a semigroup is introduced by exploiting generalized Green’s relations
L*
and
R*
, and some characterizations of fuzzy *–ideals on an arbitrary semigroup are obtained. Our main purpose is to establish the relationship between fuzzy *–ideals and abundance for an arbitrary semigroup. As an application of our results, we also give some new necessary and sufficient conditions for an arbitrary semigroup to be regular and inverse, respectively.
