Subrings of endomorphism rings associated with right minimal morphisms

Abstract

Let be a right minimal epimorphism. We prove that there exists a ring isomorphism between two rings and . We use this ring isomorphism to figure out the properties of from under the properties such as N is a fully coinvariant quotient of M (namely, is a fully invariant submodule of M), or when N is automorphism-covariant quotient of M (namely, is invariant under automorphisms of M).