论文标题
莫里塔代数的表征
A characterisation of Morita algebras in terms of covers
论文作者
论文摘要
A pair $(A, P)$ is called a cover of $\operatorname{End}_A(P)^{op}$ if the Schur functor $\operatorname{Hom}_A(P, -)$ is fully faithful on the full subcategory of projective $A$-modules, for a given projective $A$-module $P$.根据定义，莫里塔代数是自注明代数的封面，然后$ p $是一个忠实的投射注射模块。相反，我们表明$ a $是莫里塔代数，$ \ operatorName {end} _a（p）^{op} $每当$（a，p）$都是$ \ operatatornamame {end end} _a（end} _a（p）_a（p）^{p）^{op} $的封面时，都是自注明的。
A pair $(A, P)$ is called a cover of $\operatorname{End}_A(P)^{op}$ if the Schur functor $\operatorname{Hom}_A(P, -)$ 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 $\operatorname{End}_A(P)^{op}$ is self-injective whenever $(A, P)$ is a cover of $\operatorname{End}_A(P)^{op}$ for a faithful projective-injective module $P$.
