Commutative endomorphism rings

Samuel Harry Cox, Jr.

Vol. 45 (1973), No. 1, 87–91

DOI: 10.2140/pjm.1973.45.87

Abstract

Two problems of W. V. Vasconcelos are partially solved: (1) The total quotient ring of a commutative noetherian ring R is quasi-frobenius if and only if End_R(A) is commutative for each ideal A of R. (2) Let R be a commutative quasiregular ring and E a finitely presented R-module. If E is faithful and End_R(E) is semi-prime, then E is isomorphic to an ideal of R. Only commutative rings with unit and unital modules are considered.

Mathematical Subject Classification 2000

Primary: 13C10

Milestones

Received: 7 December 1971

Published: 1 March 1973