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ArticleOriginal scientific text

Title

Nil-extensions of completely simple semirings

Authors 1, 1

Affiliations

  1. Department of Mathematics, University of Burdwan, Golapbag, Burdwan - 713104, West Bengal, India

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.

Keywords

ENG
ideal extension, nil-extension, bi-ideal, completely Archimedean semirings, completely simple semiring

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Discussiones Mathematicae - General Algebra and Applications
2013/33/2
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Pages:
201-209
Main language of publication
English
Received
2013-04-23
Accepted
2013-05-02
Published
2013

DOI: 10.7151/dmgaa.1206

Exact and natural sciences