Primitive involution rings

Abstract

A *-primitive involution ring Ris either a left and right primitive ring or a certain subdirect sum of a left primitive and a right primitive ring with involution exchanging the components. An example is given of a left and right primitive ring which admits no row and column finite matrix representation. We characterize *-primitive involution rings in terms of maximal *-biideals. A *-prime involution ring has a minimal left ideal if and only if it has a minimal *-biideal, and these involution rings are always *-primitive.