On Union of Regular Near-rings
Rings and Algebras
2025-07-10 v1
Abstract
'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting of seminearrings in [[16], Mukherjee (Pal) et al., Semigroup Forum (2018)]. In it, a class of seminearrings (called generalized left completely regular seminearrings, abbreviated as GLCR) has been characterized as a union of near-rings. This work has been extended in the present article to characterize the seminearrings which are union of various types (regular, completely regular, inverse, Clifford) of regular near-rings.
Keywords
Cite
@article{arxiv.2507.06572,
title = {On Union of Regular Near-rings},
author = {Rajlaxmi Mukherjee and Tuhin Manna and Kamalika Chakraborty and Sujit Kumar Sardar},
journal= {arXiv preprint arXiv:2507.06572},
year = {2025}
}