tCG Torsion Pairs

2016/10/20 by Daniel Bravo, Bravo, Daniel, Carlos E. Parra +1
Mathematics · #Rings, Modules, and Algebras #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1610.06509

Abstract

We investigate conditions for when the t-structure of Happel-Reiten-Smalø associated to a torsion pair is a compactly generated t-structure. The concept of a tCG torsion pair is introduced and for any ring R, we prove that t=(T,F) is a tCG torsion pair in R-Mod if, and only if, there exists, \T_λ\ a set of finitely presented R-modules in T, such that F=\bigcap Ker(Hom_R(T_λ,?)). We also show that every tCG torsion pair is of finite type, and show that the reciprocal is not true. Finally, we give a precise description of the tCG torsion pairs over Noetherian rings and von Neumman regular rings.

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