Algebra Seminar
An alternative perspective on projectivity of modules, by Joe Mastromatteo (Ohio University)
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When 
Nov 22, 2013 from 04:10 PM to 05:05 PM 
Where  Morton 127 
Contact Name  Sergio R. LopezPermouth 
Contact Phone  7405931258 
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Abstract: We approach the analysis of the extent of the projectivity of modules from a fresh perspective as we introduce the notion of relative subprojectivity. A module M and is said to be Nsubprojective if for every epimorphism \(g:B \rightarrow N\) and homomorphism \(f:M \rightarrow N\), there exists a homomorphism \(h:M \rightarrow B\) such that \(gh=f\). For a module M, the subprojectivity domain of M is defined to be the collection of all modules N such that M is Nsubprojective. We consider, for every ring R, the subprojective profile of R, namely, the class of all subprojectivity domains for R modules. We show that the subprojective profile of R is a semilattice, and consider when this structure has coatoms or a smallest element. Modules whose subprojectivity domain is smallest as possible will be called subprojectively poor (sppoor) or projectively indigent (pindigent) and those with coatomic subprojectivy domain are said to be maximally subprojective. While we do not know if sppoor modules and maximally subprojective modules exist over every ring, their existence is determined for various families. For example, we determine that artinian serial rings have sppoor modules and attain the existence of maximally subprojective modules over the integers and for arbitrary Vrings. This work is a natural continuation to recent papers that have embraced the systematic study of the injective, projective and subinjective profiles of rings. (This talk is based on joint work of Holston, LopezPermouth, Mastromatteo and SimentalRodriguez.)