The Stacks project

Definition 11.2.3. Let $A$ be a $k$-algebra. We say an $A$-module $M$ is simple if it is nonzero and the only $A$-submodules are $0$ and $M$. We say $A$ is simple if the only two-sided ideals of $A$ are $0$ and $A$.

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View Definition 11.2.3 as pdf