Fuzzy primary representations of fuzzy ideals

D. S. Malik; John N. Mordeson

doi:10.1016/0020-0255(91)90011-I

Fuzzy primary representations of fuzzy ideals

D. S. Malik, John N. Mordeson

Department of Mathematics

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

26 Scopus citations

Abstract

Let R be a commutative ring with identity, and let A be a fuzzy ideal of R. Then A is said to have a fuzzy primary representation if A is the intersection of a finite number of fuzzy primary ideals. We show that every fuzzy ideal A of R such that A(0) = 1 has a fuzzy primary representation if and only if R is artinian. We show that uniqueness properties for reduced primary representations of ideals (in the usual sense) carry over to fuzzy ideals.

Original language	English (US)
Pages (from-to)	151-165
Number of pages	15
Journal	Information sciences
Volume	55
Issue number	1-3
DOIs	https://doi.org/10.1016/0020-0255(91)90011-I
State	Published - Jun 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)90011-I

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abstract = "Let R be a commutative ring with identity, and let A be a fuzzy ideal of R. Then A is said to have a fuzzy primary representation if A is the intersection of a finite number of fuzzy primary ideals. We show that every fuzzy ideal A of R such that A(0) = 1 has a fuzzy primary representation if and only if R is artinian. We show that uniqueness properties for reduced primary representations of ideals (in the usual sense) carry over to fuzzy ideals.",

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AB - Let R be a commutative ring with identity, and let A be a fuzzy ideal of R. Then A is said to have a fuzzy primary representation if A is the intersection of a finite number of fuzzy primary ideals. We show that every fuzzy ideal A of R such that A(0) = 1 has a fuzzy primary representation if and only if R is artinian. We show that uniqueness properties for reduced primary representations of ideals (in the usual sense) carry over to fuzzy ideals.

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Fuzzy primary representations of fuzzy ideals

Abstract

All Science Journal Classification (ASJC) codes

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