On 𝑃-Coherent Endomorphism Rings

Proceedings Mathematical Sciences

Li-Xin Mao¹ 

[1] Institute of Mathematics, Nanjing Institute of Technology, Nanjing , People’s Republic of China$$

关键词: 𝑃-coherent ring;    𝑃𝑃 ring;    torsionfree module;    divisible module;    precover;    preenvelope;    pseudokernel;    pseudocokernel.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown