模的投射覆盖、内射包络与局部环  

Projective Covers,Injective Envelopes and Local Rings

作　　者：何东林[1] 李煜彦[1] HE Dong-lin;LI Yu-yan(School of Mathematics and Information Sciences,Longnan Teachers College,Longnan Gansu 742500,China)

机构地区：[1]陇南师范高等专科学校数信学院

出　　处：《佳木斯大学学报（自然科学版）》2020年第1期165-167,共3页Journal of Jiamusi University：Natural Science Edition

基　　金：甘肃省高等学校科研项目(2018A-269);甘肃省高等学校创新能力提升项目(2019B-224)

摘　　要：利用环模理论和同调代数的方法,研究了模的投射覆盖、内射包络与局部环之间的关系.设Q是一个投射-内射左R-模.证明了如果同态f:Q→X是非投射模_RX的投射覆盖且自同态环End(RX)为局部环,那么包含同态i:Kerf→Q为Kerf的内射包络;如果同态f:Y→Q是非内射模RY的内射包络且自同态环End(RY)为局部环,那么标准投射π:Q→Cokerf为Cokerf的投射覆盖.结果表明,模的投射覆盖、内射包络与局部环之间有着密切的联系.Using methods of rings and modules, and homology algebras, the paper investigates the relationship between projective covers, injective envelopes of modules and local rings. Let Q be a projective-injective left R-module. We prove that if a homomorphism f:Q→X is projective cover of non-projective module RX, and endomorphism ring End(RX) is a local ring, then the inclusion homomorphism i:Kerf→Q is injective envelope of Kerf;If a homomorphism f:Y→Q is injective envelope of non-injective module _RY, and endomorphism ring End(RY) is a local ring, then the standard projective π:Q→ Cokerg is projective cover of Cokerg. The results indicate that there are closely relationships between projective covers, injective envelopes of modules and local rings.

关 键 词：投射覆盖 内射包络 局部环 不可分解模 

分 类 号：O153.3[理学—数学]