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 (submodules) are a notion dual to essential monomorphisms (submodules); 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 November 17, 2023 at 10:14:54. See the history of this page for a list of all contributions to it.