A note on quasi-Frobenius rings

Edgar Earle Enochs

Vol. 24 (1968), No. 1, 69–70

DOI: 10.2140/pjm.1968.24.69

Abstract

Morita and Curtis proved independently that if A is a quasi-Frobenius ring and P_a^∨ finitely generated, projective, faithful, left A-module, then the ring of endomorphisms B = End_A(P) is quasi-Frobenius and P is a finitely generated, projective, faithful, left B-module. It also turns out that A≅End_B(P). We prove a theorem implying that every quasi-Frobenius ring can be represented as such a ring of endomorphisms.

Mathematical Subject Classification

Primary: 16.40

Milestones

Received: 28 February 1967

Published: 1 January 1968