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A Characterisation of Morita Algebras in Terms of Covers
Algebras and Representation Theory ( IF 0.5 ) Pub Date : 2021-06-04 , DOI: 10.1007/s10468-021-10064-8 Tiago Cruz
中文翻译:
Morita 代数在覆盖方面的刻画
更新日期:2021-06-04
Algebras and Representation Theory ( IF 0.5 ) Pub Date : 2021-06-04 , DOI: 10.1007/s10468-021-10064-8 Tiago Cruz
A pair (A, P) is called a cover of EndA(P)op if the Schur functor HomA(P,−) is fully faithful on the full subcategory of projective A-modules, for a given projective A-module P. By definition, Morita algebras are the covers of self-injective algebras and then P is a faithful projective-injective module. Conversely, we show that A is a Morita algebra and EndA(P)op is self-injective whenever (A, P) is a cover of EndA(P)op for a faithful projective-injective module P.
中文翻译:
Morita 代数在覆盖方面的刻画
一对(甲,P)被称为端部的盖甲(P)ø p如果舒尔算符坎甲(P - )是上投影的满子完全忠实甲-模块,对于给定的投影甲-模P。根据定义,森田代数是自射代数的覆盖,然后P是一个忠实的射影-射模。相反,我们证明A是 Morita 代数并且 End A ( P ) o p是自射的,只要 ( A ,P)是端部的盖甲(P)ø p为忠实投影-射模P。