摘要
通过极小满的性质,讨论一个范畴A的(半)完全性与它的推出范畴Aout的(半)完全性之间的关系,得到了一个范畴A是(半)完全范畴当且仅当Aout也是(半)完全范畴,并将其应用到环上,得到了一个环是(半)完全的当且仅当它的推出诱导环是(半)完全的.
The relationships between the (semi-)perfect properties of Abelian categories and the (semi-) perfect properties of its pushout categories through the properties of minimal epimorphism are discussed, and the main result is obtained as follow: the category Ais (semi-)perfect if and only if the one Aout is (semi-)perfect. As an application, the ring A is (semi-)perfect if and only if the ring B, which is induced by A, is (semi-) perfect.
出处
《福建师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2015年第1期1-5,共5页
Journal of Fujian Normal University:Natural Science Edition
基金
国家自然科学基金资助项目(11071040)
福建省自然科学基金资助项目(2010J01001)
关键词
投射盖
推出范畴
(半)完全范畴
(半)完全环
projective cover
pushout category
(semi-) perfect category
(semi-) perfect ring