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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1206,
author = {Sunil K. Maity and Rituparna Ghosh},
title = {Nil-extensions of completely simple semirings},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {33},
year = {2013},
pages = {201-209},
zbl = {1301.16054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1206}
}
Sunil K. Maity; Rituparna Ghosh. Nil-extensions of completely simple semirings. Discussiones Mathematicae - General Algebra and Applications, Tome 33 (2013) pp. 201-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1206/
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