Year: 2026
Type: preprint
Abstract: Let $S$ be an isosimple module, that is, a nonzero module isomorphic to every nonzero submodule of itself. In this paper, we investigate if the square $S^2 := S \oplus S$ is isoantian when $S$ is an isosimple module. If the base ring is commutative, then the answer is yes. However, for noncommutative rings this is no longer true even when $\mathrm{End}_R(S)$ is a discrete valuation ring. We also give some positive results coming from quasi-projectivity and Morita equivalence. Finally, we consider when every finite powers of an isosimple module are isoantian provided it holds for the square. Our related result says that if $S^2$ is isoantian and $E = \mathrm{End}_R(S)$ is either commutative Noetherian or right semihereditary, then every finite power of $S$ is isoantian.
Source: arXiv (Cornell University)
Authors: Yan, Ran, Zhang, Xiaolei
Institution: Tianshui Normal University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223106565