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 (US) |
|---|---|
| Pages (from-to) | 237-250 |
| Number of pages | 14 |
| Journal | Information sciences |
| Volume | 53 |
| Issue number | 3 |
| DOIs | |
| State | Published - Feb 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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Cite this
Malik, D. S., & Mordeson, J. N. (1991). Fuzzy maximal, radical and primary ideals of a ring. Information sciences, 53(3), 237-250. https://doi.org/10.1016/0020-0255(91)90038-V