Year: 2025
Type: article
Abstract: As it is well known, modules are a common generalization of vector spaces, abelian groups, and rings. The definition of a module is obtained by replacing the term ‘field’ in the set of conditions defining a vector space with an arbitrary ring. In this paper, we prove that the abelianity (commutativity) property of the group structure of a unitary module over an arbitrary ring with identity can be recovered from the remaining conditions.
Author: Nuray Eroğlu
Institution: Tekirdağ Namık Kemal University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4408418858