Vol. 45, No. 1, 1973

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Commutative endomorphism rings

Samuel Harry Cox, Jr.

Vol. 45 (1973), No. 1, 87–91
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 EndR(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 EndR(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
Authors
Samuel Harry Cox, Jr.