### 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) |
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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