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 |
|---|---|
| Pages (from-to) | 237-250 |
| Number of pages | 14 |
| Journal | Information Sciences |
| Volume | 53 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1991 |
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All Science Journal Classification (ASJC) codes
- Artificial Intelligence
- Computer Science Applications
- Information Systems
- Information Systems and Management
- Statistics, Probability and Uncertainty
- Electrical and Electronic Engineering
- Statistics and Probability
Cite this
Fuzzy maximal, radical and primary ideals of a ring. / Malik, Davender S.; Mordeson, John N.
In: Information Sciences, Vol. 53, No. 3, 1991, p. 237-250.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Fuzzy maximal, radical and primary ideals of a ring
AU - Malik, Davender S.
AU - Mordeson, John N.
PY - 1991
Y1 - 1991
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=0026112773&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0026112773&partnerID=8YFLogxK
U2 - 10.1016/0020-0255(91)90038-V
DO - 10.1016/0020-0255(91)90038-V
M3 - Article
AN - SCOPUS:0026112773
VL - 53
SP - 237
EP - 250
JO - Information Sciences
JF - Information Sciences
SN - 0020-0255
IS - 3
ER -