Affiliation:
1. Department of Mathematics, Yasouj University, Yasouj, Iran
Abstract
In this paper, we introduce the concept of [Formula: see text]-semisimple modules. We prove that a multiplication reduced module is [Formula: see text]-semisimple if and only if it is a Baer module. We show that a large family of abelian groups are [Formula: see text]-semisimple. Furthermore, we give a topological characterizations of type submodules (ideals) of multiplication reduced modules ([Formula: see text]-semisimple rings). Moreover, we observe that there is a one-to-one correspondence between type ideals of some algebraic structures on one hand and regular closed subsets of some related topological spaces on the other hand. This also characterizes the form of closed ideals in [Formula: see text].
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
1 articles.
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1. On parallel Krull dimension of modules;Communications in Algebra;2022-06-14