nLab superfluous epimorphism

Idea

Given a ring $R$ (or some analogue, say a Banach algebra), a submodule $K$ of an $R$-module $M$ is called superfluous or small in $M$, written $K \ll M$, if, for every submodule $L\subset M$ , the equality $K + L = M$ implies $L = M$. An epimorphism $f : M\to N$ is called superfluous (or coessential) if $Ker f \ll M$.

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.

References

• Robert Wisbauer, Foundations of module and ring theory, pdf

category: algebra