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An essential epimorphism is a surjection with superfluous kernel, and a projective cover is a projective source with such a map
Definition
An essential epimorphism of modules is a surjective homomorphism whose kernel is superfluous: whenever and , one already has .
A projective cover of is an essential epimorphism with projective in the sense of Projective modules and the lifting property and Equivalent characterizations of projective modules.
The superfluous-kernel language is the one used on this page, motivated by For a finite-length module, the radical is a superfluous submodule.
Depends on
Used by
- Superfluous subobjects and projective covers in an abelian category Definition
- A nonsplit simple has Hom-pairing diagonal two Example
- The dual numbers have Cartan map multiplication by two Example
- Filtered projectives prove canonical basic-set reciprocity Lemma
- Finite-dimensional graded algebras have graded projective covers Lemma
- Fitting decomposition in a finite-length abelian category Lemma
- Projective covers in O are indecomposable and unique Proposition
- Category O has enough projectives Theorem
- Every finite-dimensional module has a projective cover, unique up to isomorphism over the target Theorem
- Finite-Weyl canonical basic sets from Lusztig properties Theorem
- Indecomposable projective classes form a basis of split K0 Theorem
- Projective and simple classes are dual bases under splitting Theorem
Dependency tree · two levels
13 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Peter Webb, A Course in Finite Group Representation Theory (23 Feb 2016 draft) (standard reference, not scraped)