A pair (A, P) is called a cover of End_A(P)^op if the Schur functor Hom_A(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 End_A(P)^op is self-injective whenever (A, P) is a cover of End_A(P)^op for a faithful projective-injective module P.

中文翻译：

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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。