Bi-ideals in k-regular and intra k-regular semirings

Anjan K. Bhuniya; Kanchan Jana

Discussiones Mathematicae - General Algebra and Applications (2011)

  • Volume: 31, Issue: 1, page 5-23
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Anjan K. Bhuniya, and Kanchan Jana. "Bi-ideals in k-regular and intra k-regular semirings." Discussiones Mathematicae - General Algebra and Applications 31.1 (2011): 5-23. <http://eudml.org/doc/276570>.

@article{AnjanK2011,
abstract = {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.},
author = {Anjan K. Bhuniya, Kanchan Jana},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {k-bi-ideals; k-ideals; semiprimary subsets; k-regular semirings; intra k-regular semirings; quasi -ideals; -regular semirings; intra regular semirings; -bi-ideals},
language = {eng},
number = {1},
pages = {5-23},
title = {Bi-ideals in k-regular and intra k-regular semirings},
url = {http://eudml.org/doc/276570},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Anjan K. Bhuniya
AU - Kanchan Jana
TI - Bi-ideals in k-regular and intra k-regular semirings
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2011
VL - 31
IS - 1
SP - 5
EP - 23
AB - 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.
LA - eng
KW - k-bi-ideals; k-ideals; semiprimary subsets; k-regular semirings; intra k-regular semirings; quasi -ideals; -regular semirings; intra regular semirings; -bi-ideals
UR - http://eudml.org/doc/276570
ER -

References

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