满子范畴的反变有限性与同调满同态  

The contravariant finiteness of the full subcategories and the homological epimorphisms

作　　者：连颖颖[1] 彭桢[1] 沈燕[2] LIAN Yingying;PENG Zhen;SHEN Yan(School of Mathematics and Statistics,Anyang Normal University,Anyang 455000,China;School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安阳师范学院数学与统计学院,河南安阳455000 [2]安徽大学数学科学学院,安徽合肥230601

出　　处：《安徽大学学报（自然科学版）》2018年第6期57-59,共3页Journal of Anhui University(Natural Science Edition)

基　　金：国家青年自然科学基金资助项目(11401011);河南省高校重点科研项目(16A110027)

摘　　要：讨论域k上的代数A,B的满子范畴p<∞(A)和p<∞(B)的关系,研究它们的反变有限性之间的关系,得到结论:如果域k上的代数A,B之间存在同调满同态φ:A→B,若B作为A-模是投射维数有限的,则p<∞(A)反变有限可以推出p<∞(B)也反变有限.This paper studied the relation of the full subcategories p^<∞(A)and p^<∞(B)of A-mod and B-mod,and the relation of the contravariant finiteness of p^<∞(A)and p^<∞(B).The following result was proved.Let A,B be two algebras over the field k,if the projective dimension of B was finite as an A-module and p^<∞(A)was contravariantly finite in A-mod,then p^<∞(B)was contravariantly finite in B-mod.

关 键 词：同调满同态 满子范畴 反变有限 右逼近 

分 类 号：O153.3[理学—数学]