Bhavanari, Satyanarayana and Kuncham, Syam Prasad and Jupudi, Lakshmi Ram Prasad
(2009)
*Fuzzy Cosets of Prime Fuzzy Submodules.*
The Journal of Fuzzy Mathematics, 17 (3).
ISSN 1066-8950

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## Abstract

Let R be a fixed (not necessarily commutative) ring with identity, and M a unitary left R -module. Some fundamental results related to the concepts “fuzzy cosets of prime fuzzy submodules” were proved. The quotient module M m is a prime module whenever m is a prime fuzzy submodule. Conversely, if m is a fuzzy submodule attaining exactly two values, and the quotient module M m is prime then the given fuzzy submodule m is prime. Finally, it is proved that if m is a fuzzy submodule of M then there exists an order preserving mapping between the sets P and Q where P is the set of all prime fuzzy submodules s of m with m Õs and s (0) = m (0) ; and Q is the set of al prime fuzzy submodules q of the quotient module M m with qm Õq and qm =q (0) .

Item Type: | Article |
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Additional Information: | © 2009 International Fuzzy Mathematics Institute Los Angeles |

Uncontrolled Keywords: | Prime submodule, fuzzy submodule, prime fuzzy submodule, fuzzy cosets of a fuzzy submodule. |

Subjects: | Engineering > MIT Manipal > Mathematics |

Depositing User: | MIT Library |

Date Deposited: | 08 Dec 2011 06:53 |

Last Modified: | 06 Mar 2013 04:35 |

URI: | http://eprints.manipal.edu/id/eprint/1703 |

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