# 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

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topSunil 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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