Prime fuzzy ideals over noncommutative rings
Rings and Algebras
2016-10-26 v2
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.
Cite
@article{arxiv.1012.5575,
title = {Prime fuzzy ideals over noncommutative rings},
author = {Gabriel Navarro and Oscar Cortadellas and F. J. Lobillo},
journal= {arXiv preprint arXiv:1012.5575},
year = {2016}
}
Comments
Section 1 has been rewritten, corrected typos, added references