nLab superfluous epimorphism




Given a ring RR (or some analogue, say a Banach algebra), a submodule KK of an RR-module MM is called superfluous or small in MM, written KMK \ll M, if, for every submodule LML\subset M , the equality K+L=MK + L = M implies L=ML = M. An epimorphism f:MNf : M\to N is called superfluous (or coessential) if KerfMKer f \ll M.

Superfluous epimorphisms are a notion dual to essential monomorphisms; their role in the study of projective covers is analogous to the role of essential monomorphisms in the study of injective envelopes.


category: algebra

Last revised on July 5, 2024 at 17:20:22. See the history of this page for a list of all contributions to it.