Fuzzy maximal, radical and primary ideals of a ring

D. S. Malik; John N. Mordeson

doi:10.1016/0020-0255(91)90038-V

Fuzzy maximal, radical and primary ideals of a ring

D. S. Malik, John N. Mordeson

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

Abstract

We introduce the concepts of fuzzy maximal ideal, the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring. We show that a fuzzy left (right) ideal A of a ring R is a fuzzy maximal ideal if and only A(0) = 1 and A_* = {x ε{lunate} R:A(x) = A(0)} is a maximal left (right) ideal of R. We also show that a fuzzy ideal A of a commutative ring R with unity is a fuzzy primary ideal of R if and only A(0) = 1, A is two-valued and A_* is a primary ideal of R.

Original language	English (US)
Pages (from-to)	237-250
Number of pages	14
Journal	Information sciences
Volume	53
Issue number	3
DOIs	https://doi.org/10.1016/0020-0255(91)90038-V
State	Published - Feb 1991

All Science Journal Classification (ASJC) codes

Software
Control and Systems Engineering
Theoretical Computer Science
Computer Science Applications
Information Systems and Management
Artificial Intelligence

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10.1016/0020-0255(91)90038-V

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AB - We introduce the concepts of fuzzy maximal ideal, the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring. We show that a fuzzy left (right) ideal A of a ring R is a fuzzy maximal ideal if and only A(0) = 1 and A* = {x ε{lunate} R:A(x) = A(0)} is a maximal left (right) ideal of R. We also show that a fuzzy ideal A of a commutative ring R with unity is a fuzzy primary ideal of R if and only A(0) = 1, A is two-valued and A* is a primary ideal of R.

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Fuzzy maximal, radical and primary ideals of a ring

Abstract

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