On \b{L}-fuzzy multiplication modules

Shahabaddin Ebrahimi Atani, Fatemeh Esmaeili Khalil Saraei
2017 Discussiones Mathematicae - General Algebra and Applications  
Let L be a complete lattice. In a manner analogous to a commutative ring, we introduce and investigate the L-fuzzy multiplication modules over a commutative ring with non-zero identity. The basic properties of the prime L-fuzzy submodules of L-fuzzy multiplication modules are characterized. I = (N : M ) = {r ∈ R : rm ⊆ N }. The literature on multiplication ideals and modules is quite extensive, for example, see [1, 2, 4, 6, 7] and [16] . In particular [2, 7] , and [16] contain a number of
more » ... n a number of characterizations of multiplication modules. Research on the theory of fuzzy sets has been witnessing an exponential growth; both within mathematics and in its applications. This ranges from traditional mathematical like logic, topology, algebra, analysis etc. to pattern recognition, information theory, artificial intelligence, neural networks and planning. Consequently, fuzzy set theory has emerged as a potential area of interdisciplinary research and fuzzy module theory is of recent interest. In the last few years a considerable amount of work has been done on fuzzy modules. Zadeh in [17] introduced the notion of a fuzzy subset µ of a non-empty set X as a function from X to [0, 1]. Goguen in [8] generalized the notion of fuzzy sets of X to a lattice L. In [14] , Rosenfeld considered the fuzzification of algebraic structures. Liu [10] introduced and examined the notion of a fuzzy ideal of a ring. Since then several authors have obtained interesting results on L-fuzzy ideals of a ring and L-fuzzy modules (see [3, 4, 5, 9, 11] and [14]). See also [12] for a comprehensive survey of the literature of these developments. Hence the study of the L-fuzzy multiplication modules theory is worthy of study.
doi:10.7151/dmgaa.1268 fatcat:haakjm63xnavtlmb22nlkzumde