NON-POINTED EXACTNESS, RADICALS, CLOSURE OPERATORS

Abstract

AbstractIn this paper it is shown how nonpointed exactness provides a framework which allows a simple categorical treatment of the basics of Kurosh–Amitsur radical theory in the nonpointed case. This is made possible by a new approach to semi-exactness, in the sense of the first author, using adjoint functors. This framework also reveals how categorical closure operators arise as radical theories.