On commutative endomorphism rings

Wolmer Vasconcelos

Vol. 35 (1970), No. 3, 795–798

DOI: 10.2140/pjm.1970.35.795

Abstract

This note deals with a finitely generated faithful module E over a commutative semi-prime noetherian ring R, with commutative endomorphism ring Hom_R(E,E) = Ω(E). It is shown that E is identifiable to an ideal of R whenever Ω(E) lacks nilpotent elements; a class of examples with Ω(E) commutative but not semi-prime is discussed.

Mathematical Subject Classification

Primary: 13.40

Milestones

Received: 3 March 1970

Published: 1 December 1970