Endomorphism rings via minimal morphisms

Abstract

We prove that if u : K → M is a left minimal extension, then there exists an isomorphism between two subrings, EndM R (K) and EndK R (M) of EndR(K) and EndR(M) respectively, modulo their Jacobson radicals. This isomorphism is used to deduce properties of the endomorphism ring of K from those of the endomorphism ring of M in certain situations such us when K is invariant under endomorphisms of M, or when K is invariant under automorphisms of M.