Prime fuzzy ideals over noncommutative rings

Details Prime fuzzy ideals over noncommutative rings Prime fuzzy ideals over noncommutative rings

2010-12-27

arxiv.org/abs/1012.5575v2

Mathematics

Rings and Algebras

Section 1 has been rewritten, corrected typos, added references

Scientific paper

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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