Abstract

We investigate conditions when the t-structure of Happel-Reiten-Smalo 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-lambda} a set of finitely presented R-modules in T, such that F = boolean AND Ker(Hom(R) (T-lambda, ?)). 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.