Modules Whose Endomorphism Rings Are (m, n)-Coherent  

作　　者：Xiaoqiang Luo Lixin Mao 

机构地区：[1]Department of Mathematics, Sichuan University of Arts and Science Dazhou, Sichuan 635000, China [2]Department of Mathematics and Physics, Nanjing Institute of Technology Nanjing 211167, China

出　　处：《Algebra Colloquium》2019年第2期231-242,共12页代数集刊（英文版）

摘　　要：Let M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of S. It is shown that S is a left (m, n)-coherent ring if and only if the left annihilator annMn(S)(X)annMn(S)(X) is a finitely generated left ideal of Mn(S) for any M-m-generated submodule X of M^n if and only if every M-(n, m)-presented right R-module has an add M-preenvelope. As a consequence, we investigate when the endomorphism ring S is left coherent, left pseudo-coherent, left semihereditary or von Neumann regular.

关 键 词：M-(m n)-flat module (m n)-coherent RING n-semihereditary RING PREENVELOPE 

分 类 号：O1[理学—数学]