It is well known that a semigroup S is a Clifford semigroup if and only if S is a strong semilattice of groups. We have recently extended this important result from semigroups to semirings by showing that a semiring S is a Clifford semiring if and only if S is a strong distributive lattice of skew-rings. In this paper, we introduce the notions of Clifford semidomain and Clifford semifield. Some structure theorems for these semirings are obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1080,
author = {Mridul K. Sen and Sunil K. Maity and Kar-Ping Shum},
title = {Clifford semifields},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {24},
year = {2004},
pages = {125-135},
zbl = {1067.16071},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1080}
}
Mridul K. Sen; Sunil K. Maity; Kar-Ping Shum. Clifford semifields. Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004) pp. 125-135. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1080/
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