3
$\begingroup$

Suppose that $R$ is a finite dimensional $k$-algebra. I say that $R$ is Frobenius if it is locally bounded (see this question for a definition) and indecomposable projectives and injectives coincide. Could you help me to prove the following:

$R$ is Frobenius if and only if $_RR$ is injective as an $R$-module.

Of course if $R$ is Frobenius then $_RR$ is injective as an $R$-module, how can I prove the converse?

  • 0
    Where does this notation come from? It seems non-standard to call $R$ Frobenius and not self-injective or quasi-Frobenius.2012-11-05
  • 0
    it is from the book of happel "triangulated categories in the representation theory of finite dimensional algebras"2012-11-06

1 Answers 1