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Fuzzy Cosets of Prime Fuzzy Submodules

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
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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