RELATIVE PROJECTIVITY AND RELATED RESULTS
Copyright policy )RELATIVE PROJECTIVITY AND RELATED RESULTS
Summary: Let \(R\) be a commutative Noetherian ring and let \(M\) be an Artinian \(R\)-module. Let \(M''\subseteq M'\) be submodules of \(M\). Suppose \(F\) is an \(R\)-module which is projective relative to \(M\). Then it is shown that \[ \text{Att}_R(\text{Hom}_A (F,M'):_{\text{Hom}_A(F,M)}I^n),\;n\in\mathbb{N} \] and \[ \text{Att}_R(\text{Hom}_A (F,M'):_{\text{Hom}_A(F,M)}I^n/\text{Hom}_A(F,M''): _{\text{Hom}_A(F,M)}I^n),\;n\in\mathbb{N} \] are ultimately constant.
relative projective module, Commutative Artinian rings and modules, finite-dimensional algebras, Artinian module, Projective and free modules and ideals in commutative rings, Commutative Noetherian rings and modules
relative projective module, Commutative Artinian rings and modules, finite-dimensional algebras, Artinian module, Projective and free modules and ideals in commutative rings, Commutative Noetherian rings and modules
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!