Extended Algebraic Structure of Quasimodules
Year: 2025
Type: article
Abstract: A Module is one of the common and significant algebraic structures of modern algebra. We have introduced in our paper “An Associated Structure of a Module” published in Revista de la Academia Canaria de Ciencias, Volume XXV, 9–22 (2013), the concept of a quasimodule which is a generalisation of a module that speaks of a topological hyperspace structure as well as a module structure in some sense. A quasimodule is a conglomeration of semigroup structure, ring multiplication and partial order; this structure always contains a module. In the present paper we shall introduce the concept of an ideal in a quasimodule. This concept is completely different from the concept of an ideal in a ring. We shall discuss several properties of ideals and construct the ideal generated by any subset of a quasimodule. We shall define a minimal ideal and find a necessary and sufficient condition for a proper ideal to be a minimal ideal.
Source: SARAJEVO JOURNAL OF MATHEMATICS
DOI: 10.5644/sjm.20.02.03
Authors: SANDIP JANA, Supriyo Jana
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409439152