A New Type Fuzzy Module over Fuzzy Rings

Abstract

A new kind of fuzzy module over a fuzzy ring is introduced by generalizing Yuan and Lee's definition of the fuzzy group and Aktaş and Çağman's definition of fuzzy ring. The concepts of fuzzy submodule, and fuzzy module homomorphism are studied and some of their basic properties are presented analogous of ordinary module theory.

A note on direct product of fuzzy modules over fuzzy rings

“…(1)- (4), the definitions of the concept of fuzzy group, fuzzy ring and fuzzy module is given in, [5], [3], [8]. …”

“…In these approach, while the set is assumed to be nonfuzzy, the binary operation is fuzzy. By the use of these fuzzy group and fuzzy ring structures, the concept of fuzzy module over fuzzy ring is presented in [3].…”

“…In this work, by using the definition of fuzzy modules over fuzzy rings [3], a new kind of direct product of fuzzy is introduced and studied. Some properties of this new structure is investigated analogues of ordinary module theory.…”

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AbstractIn this paper, a new kind of direct product of fuzzy modules over fuzzy rings is studied by using the definition of new type of fuzzy modules over fuzzy rings which is introduced in [3]. Some properties of this new structure is investigated analogues to ordinary module theory.

Mathematics Subject Classification: 03E72; 08A72, 20N25

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Soft Neutrosophic Modules

“…Smarandanche and others, studied neutrosophic algebraic structures [2][3][4] by using the idea of neutrosophic theory and this was the first neutrosofication of algebraic structures. Some authors [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] have studied neutrosophic algebraic structures and nowadays, researchers are still interested in this subject. The importance of this neutrosophic structures continues to increase.…”