@misc{10481/99788,
year = {2024},
url = {https://hdl.handle.net/10481/99788},
abstract = {Simple modules on a ring have information about a part of the spectrum (the maximal
 spectrum) and, in some cases, about the whole ring. Therefore, knowledge about the
 structure and properties of simple modules is of interest. In the case we are interested
 in: chain conditions on modules relative to a multiplicative set S ⊆ A or a hereditary
 torsion theoryσ inMod- A,wefindthattwodifferentclassesoftotallysimplemodules
 appear. Given a multiplicative subset S ⊆ A one tends to introduce S-simple modules
 either as those non totally S-torsion which are S-minimal, or as those for which
 0 ⊆ M is S-maximal. Apparently these two definitions are different. We show that
 both definitions coincide, and define an A-module M to be S-simple whenever it
 satisfies: (1) Ann(M) ∩ S = ∅; (2) there exists s ∈ S such that σS(M)s = 0, and
 (3) Ms ⊆ L, for every no totally S-torsion submodule L ⊆ M. The main goal of
 this paper is to provide examples of this kind of totally simple modules by delving
 into their structure. As a byproduct we explore the relationship between these totally
 simple modules and totally prime modules, and the local behaviour of totally simple
 modules. We complete the paper by providing examples of this theory.},
publisher = {Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry},
keywords = {Simple module},
keywords = {S-finite module},
keywords = {Noetherian ring},
keywords = {Hereditary torsion  theory},
title = {Totally simple modules},
doi = {10.1007/s13366-024-00759-6},
author = {Jara Martínez, Pascual and Omar, Farah and Santos, Evangellina},
}