Finitely generated projective modules and TTF classes

Robert Wilmer Miller

Vol. 64 (1976), No. 2, 505–515

DOI: 10.2140/pjm.1976.64.505

Abstract

Let P be a finitely generated projective right A-module with trace ideal T and A-endomorphism ring B. Associated with P are the TTF classes, 𝒯_F = {⋅_AX∣P ⊗ X = 0} and 𝒯_H = {X_A∣Hom(P,X) = 0}. An investigation of these TTF classes yields characterizations of various conditions on P and T; e.g., (1) ⋅_BP is projective (flat) and (2) ⋅_AT is projective (flat). The concept of weak stability for a hereditary torsion class is introduced and characterizations are given.

Mathematical Subject Classification

Primary: 16A50, 16A50

Milestones

Received: 17 December 1975

Published: 1 June 1976