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Fuzzy Sets and Systems
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Preprint . 2010
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Fuzzy Sets and Systems
Article . 2012 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
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Prime fuzzy ideals over noncommutative rings

Prime fuzzy ideals over noncommutative rings.
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jul 2012Embargo end date: 01 Jan 2010 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 199, pages 108-120 (issn: 0165-0114, Copyright policy )
Authors: Gabriel Navarro 0001; Oscar Cortadellas; Francisco Javier Lobillo;

doi: 10.1016/j.fss.2011.11.002 , 10.48550/arxiv.1012.5575

arXiv: 1012.5575

Prime fuzzy ideals over noncommutative rings

Abstract

In this paper we introduce prime fuzzy ideals over a noncommutative ring. This notion of primeness is equivalent to level cuts being crisp prime ideals. It also generalizes the one provided by Kumbhojkar and Bapat in [Not-so-fuzzy fuzzy ideals, Fuzzy Sets and Systems 37 (1990), 237--243], which lacks this equivalence in a noncommutative setting. Semiprime fuzzy ideals over a noncommutative ring are also defined and characterized as intersection of primes. This allows us to introduce the fuzzy prime radical and contribute to establish the basis of a Fuzzy Noncommutative Ring Theory.

Section 1 has been rewritten, corrected typos, added references

Related Organizations
Keywords

Rings and Algebras (math.RA), FOS: Mathematics, Generalizations, Mathematics - Rings and Algebras, noncommutative rings, Ideals in associative algebras, semiprime fuzzy ideals, prime fuzzy ideals, 16D99, 03E72

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
13
Average
Top 10%
Top 10%
Green
bronze