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

25 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

Access to Document

10.1016/0020-0255(91)90011-I

Cite this

@article{254090b9894f4f3291ac0169e50eb42b,

title = "Fuzzy primary representations of fuzzy ideals",

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.",

author = "Malik, {D. S.} and Mordeson, {John N.}",

year = "1991",

month = jun,

doi = "10.1016/0020-0255(91)90011-I",

language = "English (US)",

volume = "55",

pages = "151--165",

journal = "Information Sciences",

issn = "0020-0255",

publisher = "Elsevier Inc.",

number = "1-3",

}

TY - JOUR

T1 - Fuzzy primary representations of fuzzy ideals

AU - Malik, D. S.

AU - Mordeson, John N.

PY - 1991/6

Y1 - 1991/6

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0026181448&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026181448&partnerID=8YFLogxK

U2 - 10.1016/0020-0255(91)90011-I

DO - 10.1016/0020-0255(91)90011-I

M3 - Article

AN - SCOPUS:0026181448

VL - 55

SP - 151

EP - 165

JO - Information Sciences

JF - Information Sciences

SN - 0020-0255

IS - 1-3

ER -

Fuzzy primary representations of fuzzy ideals

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this