The Maximal Co-Rational Extension by a Module

Abstract

Modules are S-modules where S is an arbitrary ring with or without a unit element. We consider a projective module P having a submodule K such that K + Y = P implies that the submodule Y is P (P, then, is a projective cover of P/K (Definition 4 in this section)) and we define the submodule X of P byOur main result states that up to isomorphism P/X is the maximal co-rational extension over P/K (by P/K, in the more precise wording of the title).