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 |
|---|---|
| Pages (from-to) | 111-115 |
| Number of pages | 5 |
| Journal | Fuzzy Sets and Systems |
| Volume | 37 |
| Issue number | 1 |
| DOIs | |
| State | Published - Aug 15 1990 |
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All Science Journal Classification (ASJC) codes
- Artificial Intelligence
- Computer Science Applications
- Computer Vision and Pattern Recognition
- Information Systems and Management
- Statistics, Probability and Uncertainty
- Electrical and Electronic Engineering
- Statistics and Probability
Cite this
Fuzzy ideals of artinian rings. / Malik, Davender S.
In: Fuzzy Sets and Systems, Vol. 37, No. 1, 15.08.1990, p. 111-115.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Fuzzy ideals of artinian rings
AU - Malik, Davender S.
PY - 1990/8/15
Y1 - 1990/8/15
N2 - 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.
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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UR - http://www.scopus.com/inward/citedby.url?scp=38249016991&partnerID=8YFLogxK
U2 - 10.1016/0165-0114(90)90069-I
DO - 10.1016/0165-0114(90)90069-I
M3 - Article
VL - 37
SP - 111
EP - 115
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
SN - 0165-0114
IS - 1
ER -