Vol. 35, No. 3, 1970

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On commutative endomorphism rings

Wolmer Vasconcelos

Vol. 35 (1970), No. 3, 795–798
Abstract

This note deals with a finitely generated faithful module E over a commutative semi-prime noetherian ring R, with commutative endomorphism ring HomR(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
Authors
Wolmer Vasconcelos
Rutgers University, New Brunswick
NJ
United States