PARTIAL COTILTING MODULES AND THE LATTICES INDUCED BY THEM

We study a duality between (infinitely generated) cotilting and tiltin g modules over an arbitrary ring. Dualizing a result of Bongartz, we s how that a module P is partial cotilting iff P is a direct summand of a cotilting module C such that the left Ext-orthogonal class (perpendi cular to)p coincides with C-perpendicular to. As an application, we ch aracterize all cotilting torsion-free classes. Each partial cotilting module P defines a lattice L = [Cogen P, P-perpendicular to] of torsio n-free classes. Similarly, each partial tilting module P' defines a la ttice L' = [[Gen P', P'(perpendicular to)]] of torsion classes. Genera lizing a result of Assem and Kerner, we show that the elements of L ar e determined by their Rej(p)-torsion parts, and the elements of L' by their Tr-p'-torsion-free parts.