-complemented and -supplemented modules

Proper classes of monomorphisms and short exact sequences were introduced by Buchsbaum to study relative homo- logical algebra. It was observed in abelian group theory that com- plement submodules induce a proper class of monomorphisms and this observations were extended to modules by Stenstrom, Gener- alov, and others. In this note we consider complements and supple- ments with respect to (idempotent) radicals and study the related proper classes of short exact sequences.