### 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

*Information Sciences*,

*53*(3), 237-250. https://doi.org/10.1016/0020-0255(91)90038-V

**Fuzzy maximal, radical and primary ideals of a ring.** / Malik, Davender S.; Mordeson, John N.

Research output: Contribution to journal › Article

*Information Sciences*, vol. 53, no. 3, pp. 237-250. https://doi.org/10.1016/0020-0255(91)90038-V

}

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 -