International Journal of Fuzzy Mathematics and Systems

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Fuzzy Aspects of Rings with Chain Conditions


Affiliations
1 Department of Mathematics, Girijananda Chowdhury Institute of Management and Technology, Assam-781017, India
2 Department of Mathematics, Gauhati University, Assam-781014, India
     

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Our attempt is to study fuzzy aspects of rings with chain conditions. The notion of fuzzy annihilators is used to define fuzzy Goldie ring. It is proved that the fuzzy left singular ideal of a semi-prime ring is zero. If a ring satisfies ascending chain condition (a.c.c.) on fuzzy left annihilators then its fuzzy left singular ideal is nilpotent. For a semi-prime fuzzy left Goldie ring every fuzzy essential left ideal contains a left fuzzy regular point. Moreover it is shown that under certain conditions a ring satisfies a.c.c. on fuzzy left annihilators. Finally it is proved that a fuzzy semi-prime ring with a.c.c. on fuzzy annihilator ideals has only finite number of minimal fuzzy prime ideals.

AMS subject classification: 03E72, 16P60.


Keywords

Fuzzy Ideal, Fuzzy Annihilators, Fuzzy Essential Ideal
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  • Abou-Zaid S. On fuzzy ideals and fuzzy quotient rings of a ring, Fuzzy sets and systems, 59:205–210, 1993.

  • Chatters A.W and Hazarnavis C.R. Rings with chain condition, Pitman Advanced Publishing program, 1980.

  • Kumar R. Fuzzy semiprimary ideals of rings, Fuzzy sets and systems, 42:263–272, 1991.

  • Kumar R. Fuzzy ideals and fuzzy semi-prime ideals, Some ring theoretic analogues, Information Sci., 46:43–52, 1992.

  • Kumar R. Certain fuzzy ideals of rings redefined, Fuzzy sets and systems, 46:251– 260, 1992.

  • Liu.WFuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and systems, 8:133– 139, 1982.

  • Malik D.S. Fuzzy ideals of artinian rings, Fuzzy sets and systems, 46:111–115, 1990.

  • Medhi.U, Rajkhowa. K. K, Barthakur. L. K. and Saikia H.K. On fuzzy essential ideals of rings, Advances in fuzzy sets and systems, 3(3):287–299, 2008.

  • Mukharjee T.K. and Sen M.K. Prime fuzzy ideals in rings, Fuzzy sets and systems, 32:337–341, 1989.

  • MukharjeeT. K. and Sen M. K. Rings with chain conditions, Fuzzy sets and systems, 39:117–123, 1991.

  • Rosenfeld A. Fuzzy groups, J. Math. anal. Appl., 35:512–517, 1971.

  • Zadeh L.A. Fuzzy sets, Information and Control, 8:338–353, 1965.


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  • Fuzzy Aspects of Rings with Chain Conditions

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Authors

Ujwal Medhi
Department of Mathematics, Girijananda Chowdhury Institute of Management and Technology, Assam-781017, India
Helen K Saikia
Department of Mathematics, Gauhati University, Assam-781014, India

Abstract


Our attempt is to study fuzzy aspects of rings with chain conditions. The notion of fuzzy annihilators is used to define fuzzy Goldie ring. It is proved that the fuzzy left singular ideal of a semi-prime ring is zero. If a ring satisfies ascending chain condition (a.c.c.) on fuzzy left annihilators then its fuzzy left singular ideal is nilpotent. For a semi-prime fuzzy left Goldie ring every fuzzy essential left ideal contains a left fuzzy regular point. Moreover it is shown that under certain conditions a ring satisfies a.c.c. on fuzzy left annihilators. Finally it is proved that a fuzzy semi-prime ring with a.c.c. on fuzzy annihilator ideals has only finite number of minimal fuzzy prime ideals.

AMS subject classification: 03E72, 16P60.


Keywords


Fuzzy Ideal, Fuzzy Annihilators, Fuzzy Essential Ideal

References