Vol. 54, No. 1, 1974

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Semiperfect rings with abelian adjoint group

W. K. Nicholson

Vol. 54 (1974), No. 1, 201–207
Abstract

A structure theorem is proved for semiperfect rings (possibly with no identity) which have an abelian adjoint group. This is used to give conditions when such a ring is finite or commutative. In particular, a semiperfect ring with identity is finite if its group of units is finitely generated and abelian. Additional information is obtained if the adjoint group is cyclic.

Mathematical Subject Classification
Primary: 16A48
Milestones
Received: 8 May 1973
Revised: 25 September 1973
Published: 1 September 1974
Authors
W. K. Nicholson