Fuzzy ideals of artinian rings

D. S. Malik

doi:10.1016/0165-0114(90)90069-I

Fuzzy ideals of artinian rings

D. S. Malik

Department of Mathematics

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

25 Scopus citations

Abstract

The object of this paper is to study fuzzy ideals over Artinian rings. Among others we prove that a ring with unity is left (right) Artinian if and only if every fuzzy left (right) ideal μ of R is finite valued. This gives a characterization of artinian rings in terms of fuzzy ideals. Mukherjee and Sen (1987) proved that if every fuzzy ideal of a ring with unity is finite valued then the ring is Noetherian. We give an example to show that the converse of this theorem is not true. We also show that certain results of Pan (1987) are not true.

Original language	English (US)
Pages (from-to)	111-115
Number of pages	5
Journal	Fuzzy Sets and Systems
Volume	37
Issue number	1
DOIs	https://doi.org/10.1016/0165-0114(90)90069-I
State	Published - Aug 15 1990

All Science Journal Classification (ASJC) codes

Logic
Artificial Intelligence

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10.1016/0165-0114(90)90069-I

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AB - The object of this paper is to study fuzzy ideals over Artinian rings. Among others we prove that a ring with unity is left (right) Artinian if and only if every fuzzy left (right) ideal μ of R is finite valued. This gives a characterization of artinian rings in terms of fuzzy ideals. Mukherjee and Sen (1987) proved that if every fuzzy ideal of a ring with unity is finite valued then the ring is Noetherian. We give an example to show that the converse of this theorem is not true. We also show that certain results of Pan (1987) are not true.

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Fuzzy ideals of artinian rings

Abstract

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