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Semilocal and semiregular group rings

1980
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Indagationes Mathematicae (Proceedings)
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Throughout this paper a ring will mean an associative ring with identity 1 # 0. The Jacobson radical of a ring R is denoted by J(R). A ring R is semilocal if R/J(R) is Artinian. R is called semiperfect if R/J(R) is Artinian and idempotents can be lifted modulo J(R). An element (I of a ring R is said to be regular (in the sense of von Neumann) if a ra = a for some r E R. If each element of R is regular, R is said to be a regular ring. A ring R is called semiregular if R/J(R) is regular and

doi:10.1016/1385-7258(80)90035-9
fatcat:lmbvy24p3rbo7h47zarrhg733m