Here we introduce the k-bi-ideals in semirings and the intra k-regular semirings. An intra k-regular semiring S is a semiring whose additive reduct is a semilattice and for each a ∈ S there exists x ∈ S such that a + xa²x = xa²x. Also it is a semiring in which every k-ideal is semiprime. Our aim in this article is to characterize both the k-regular semirings and intra k-regular semirings using of k-bi-ideals.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1172,
author = {Anjan K. Bhuniya and Kanchan Jana},
title = {Bi-ideals in k-regular and intra k-regular semirings},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {31},
year = {2011},
pages = {5-23},
zbl = {1254.16040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1172}
}
Anjan K. Bhuniya; Kanchan Jana. Bi-ideals in k-regular and intra k-regular semirings. Discussiones Mathematicae - General Algebra and Applications, Tome 31 (2011) pp. 5-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1172/
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