Abstract
In this study, the neutrosophic triplet G-module is introduced and the properties of neutrosophic triplet G-module are studied. Furthermore, reducible, irreducible, and completely reducible neutrosophic triplet G-modules are defined, and relationships of these structures with each other are examined. Also, it is shown that the neutrosophic triplet G-module is different from the G-module.
Highlights
Neutrosophy is a branch of philosophy, firstly introduced by Smarandache in 1980
Neutrosophic logic is a generalized form of many logics such as fuzzy logic, which was introduced by Zadeh [2], and intuitionistic fuzzy logic, which was introduced by Atanassov [3]
We show that the neutrosophic triplet G-module is different from the G-module, and we show that if certain conditions are met, every neutrosophic triplet vector space or neutrosophic triplet group can be a neutrosophic triplet G-module at the same time
Summary
Neutrosophy is a branch of philosophy, firstly introduced by Smarandache in 1980. Neutrosophy [1]. Many researchers have studied the concept of neutrosophic theory in [7,8,9,10,11,12]. Smarandache et al [22] studied the NT field and [23] the NT ring; Şahin et al [24] introduced the NT metric space, the NT vector space, and the NT normed space; Şahin et al [25] introduced the NT inner product. G-modules are algebraic structures constructed on groups and vector spaces. We study neutrosophic triplet G-Modules in order to obtain a new algebraic constructed on neutrosophic triplet groups and neutrosophic triplet vector spaces.
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