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arXiv · 1012.5575

Prime fuzzy ideals over noncommutative rings

Gabriel Navarro·Oscar Cortadellas·F. J. Lobillo
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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.

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Gabriel Navarro, Oscar Cortadellas, F. J. Lobillo. 2011-03-03. Prime fuzzy ideals over noncommutative rings. https://doi.org/10.1016/j.fss.2011.11.002

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