arXiv 1012.55752010-12math.RA

Prime fuzzy ideals over noncommutative rings

Gabriel Navarro, Oscar Cortadellas, F. J. Lobillo

备注：: Section 1 has been rewritten, corrected typos, added references
DOI：: 10.1016/j.fss.2011.11.002

英文摘要：

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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