Max-projective modules

DOI10.1142/S021949882150095XzbMATH Open1493.16004arXiv1903.05906OpenAlexW3021456870MaRDI QIDQ4998006

Author name not available (Why is that?)

Publication date: 1 July 2021

Published in: (Search for Journal in Brave)

Abstract: A right $R$-module $M$ is called max-projective provided that each homomorphism $f:MoR/I$ where $I$ is any maximal right ideal, factors through the canonical projection $pi:RoR/I$. We call a ring $R$ right almost-$QF$ (resp. right max-$QF$) if every injective right $R$-module is $R$-projective (resp. max-projective). This paper attempts to understand the class of right almost-$QF$ (resp. right max-$QF$) rings. Among other results, we prove that a right Hereditary right Noetherian ring $R$ is right almost-$QF$ if and only if $R$ is right max-$QF$ if and only if $R=SimesT$ , where $S$ is semisimple Artinian and $T$ is right small. A right Hereditary ring is max-$QF$ if and only if every injective simple right $R$-module is projective. Furthermore, a commutative Noetherian ring $R$ is almost-$QF$ if and only if $R$ is max-$QF$ if and only if $R=AimesB$, where $A$ is $QF$ and $B$ is a small ring.

Full work available at URL: https://arxiv.org/abs/1903.05906

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Max-projective modules

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4998006)