Year: 2025
Type: article
Abstract: In this work, we study some classes of modules closed under submodules, quotients, and projective covers, even if the left projective cover of an arbitrary left module not always exists. We obtain a characterization of artinian principal ideal rings when the class of left R R -modules closed under submodules and projective covers and the class of left R R -modules closed under quotients and projective covers coincide. Also, for commutative rings, we characterize noetherian rings in which every cyclic module is quasi-injective.
Source: Open Mathematics
Institution: Benemérita Universidad Autónoma de Puebla
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4409120920