Nil-extensions of completely simple semirings

Sunil K. Maity; Rituparna Ghosh

Discussiones Mathematicae - General Algebra and Applications (2013)

  • Volume: 33, Issue: 2, page 201-209
  • ISSN: 1509-9415

Abstract

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A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.

How to cite

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Sunil K. Maity, and Rituparna Ghosh. "Nil-extensions of completely simple semirings." Discussiones Mathematicae - General Algebra and Applications 33.2 (2013): 201-209. <http://eudml.org/doc/270632>.

@article{SunilK2013,
abstract = {A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.},
author = {Sunil K. Maity, Rituparna Ghosh},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {ideal extension; nil-extension; bi-ideal; completely Archimedean semirings; completely simple semiring; ideal extensions; nil-extensions; bi-ideals; completely simple semirings},
language = {eng},
number = {2},
pages = {201-209},
title = {Nil-extensions of completely simple semirings},
url = {http://eudml.org/doc/270632},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Sunil K. Maity
AU - Rituparna Ghosh
TI - Nil-extensions of completely simple semirings
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2013
VL - 33
IS - 2
SP - 201
EP - 209
AB - A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.
LA - eng
KW - ideal extension; nil-extension; bi-ideal; completely Archimedean semirings; completely simple semiring; ideal extensions; nil-extensions; bi-ideals; completely simple semirings
UR - http://eudml.org/doc/270632
ER -

References

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