• On 𝑃-Coherent Endomorphism Rings

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/118/04/0557-0567

• # Keywords

𝑃-coherent ring; $PP$ ring; torsionfree module; divisible module; precover; preenvelope; pseudokernel; pseudocokernel.

• # Abstract

A ring is called right 𝑃-coherent if every principal right ideal is finitely presented. Let $M_R$ be a right 𝑅-module. We study the 𝑃-coherence of the endomorphism ring 𝑆 of $M_R$. It is shown that 𝑆 is a right 𝑃-coherent ring if and only if every endomorphism of $M_R$ has a pseudokernel in add $M_R; S$ is a left 𝑃-coherent ring if and only if every endomorphism of $M_R$ has a pseudocokernel in add $M_R$. Some applications are given.

• # Author Affiliations

1. Institute of Mathematics, Nanjing Institute of Technology, Nanjing 211167, People’s Republic of China

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019