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Fuzzy quotient modules

Authors
Journal
Fuzzy Sets and Systems
0165-0114
Publisher
Elsevier
Publication Date
Volume
28
Issue
1
Identifiers
DOI: 10.1016/0165-0114(88)90118-2
Keywords
  • Fuzzy Module
  • Fuzzy Submodule
  • Fuzzy Quotient Module
  • Prime Submodule
  • Localization Of Rings
  • Torsion Submodule
Disciplines
  • Mathematics

Abstract

Abstract The concept of fuzzy modules was introduced in [1]. In this paper we construct fuzzy quotient modules. First, we introduce prime submodules and construct the fuzzy quotient module of an arbitrary fuzzy divisible module by its fuzzy prime submodule. Furthermore, by means of the localization of rings [2] we extend a fuzzy divisible module and its arbitrary fuzzy submodule to a large region and establish the fuzzy quotient module for the localized fuzzy modules. Finally, we construct the fuzzy quotient module for a fuzzy divisible module and its arbitrary fuzzy submodule, in a reasonable way. This generalization extends the concept of fuzzy quotient to a large number of fuzzy modules, of course, including fuzzy quotient vector spaces.

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