The nil radical of a fuzzy ideal
type: Item
instance of: scholarly article
title: The nil radical of a fuzzy ideal
zbMATH Open document ID: 0790.13007
DOI: 10.1016/0165-0114(93)90228-A
author: K. C. Gupta
author: Manoj K. Kantroo
published in: Fuzzy Sets and Systems
publication date: 1994-06-20T00:00:00Z
review text: Let \(R\) be a commutative ring. The authors define the fuzzy nil radical of an ideal. They then introduce the concept of a fuzzy semiprime ideal of \(R\) with the help of the fuzzy nil radical. A commutative regular ring is characterized by its semiprime ideals. It is shown that the intersection of all fuzzy semiprime ideals of \(R\) which contain a given fuzzy ideal \(\lambda\) is precisely the nil radical of \(\lambda\). A connection between a fuzzy semiprime ideal and the nil radical of a fuzzy ideal is thus obtained.
reviewed by: John N. Mordeson
Mathematics Subject Classification ID: 13L05
zbMATH DE Number: 516648
zbMATH Keywords: fuzzy nil radical
zbMATH Keywords: fuzzy semiprime ideal
MaRDI profile type: Publication
cites work: Fuzzy invariant subgroups and fuzzy ideals
cites work: Fuzzy maximal, radical, and primary ideals of a ring
cites work: Q5551488
cites work: Fuzzy groups
cites work: Fuzzy sets
full work available at URL: 0165-0114(93)90228-a
OpenAlex ID: W2057773054
description: scientific article; zbMATH DE number 516648