Given a ring (or some analogue, say a Banach algebra), a submodule of an -module is called superfluous or small in , written , if, for every submodule , the equality implies . An epimorphism is called superfluous (or coessential) if .
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.
Last revised on November 17, 2023 at 10:14:54. See the history of this page for a list of all contributions to it.