Grey injective modules on Rings
Subject Areas : AlgebraMasoomeh Hezarjaribi 1 , zohre habibi 2
1 - دانشگاه پیام نور، دانشکده علوم پایه، گروه ریاضی، تهران، ایران
2 - گروه آموزشی ریاضی، دانشکده علوم پایه، دانشگاه پیام نور، واحد شهریار، ایران
Keywords: Grey divisible, Grey injective, Grey module, Ring,
Abstract :
In this article, we study and examine gray modules and their properties. Initially, we define basic concepts such as gray sets and gray numbers, followed by introducing gray modules as an extension of fuzzy set theory. In this context, we analyze the categorical properties of gray modules and investigate important features such as products and coproducts within these modules. Additionally, the concept of injective gray modules is introduced, and their related properties are thoroughly analyzed. One of the key sections of this article is dedicated to the study of gray exact sequences. Gray exact sequences are employed as an effective tool for analyzing module structures and exploring the relationships between them. Furthermore, Baer's theorem for gray modules is examined in detail, highlighting its role in module theory and its applications. The article also delves into the study of divisible gray modules and analyzes their unique characteristics. Finally, this article aims to demonstrate that gray modules and gray exact sequences can serve as powerful tools in the analysis of complex systems with incomplete and uncertain data.
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