The structure of semiperfect rings with commutative Jacobson radical

Let $R$ be a semiperfect ring with commutative Jacobson radical $J(R)$, and let $R/J(R)\cong\prod_{i=1}^tL_i$, where the $L_i$ are the full matrix rings over skew fields $D_i$. In this article we prove theorems which enable us to reduce the study of the structure of $R$ to the study of the structure of local commutative rings for which each $D_i$ is a field which is a finite Galois extension of its prime subfield.
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