Abstract
An $R$-algebra $A$ is called an $E(R)$-algebra if the canonical homomorphism from $A$ to the endomorphism algebra $\mathop{\rm End}_RA$ of the $R$-module ${}_RA$, taking any $a \in A$ to the right multiplication $a_r\in \mathop{\rm End}_RA$ by $a$, is an
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