Geodesic
Nil-extensions of completely simple semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 2, pp. 201-209

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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.
Keywords: ideal extension, nil-extension, bi-ideal, completely Archimedean semirings, completely simple semiring 
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Maity, Sunil; Ghosh, Rituparna. Nil-extensions of completely simple semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 2, pp. 201-209. http://geodesic.mathdoc.fr/item/DMGAA_2013_33_2_a5/