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On commutativity of endomorphism rings of ideals

Author: S. Alamelu
Journal: Proc. Amer. Math. Soc. 37 (1973), 29-31
MSC: Primary 13E05; Secondary 16A42
MathSciNet review: 0311651
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Abstract: Let R be a commutative noetherian ring with $ {\operatorname{Hom}_R}(I,I)$ commutative for all ideals I. Then the total quotient ring of R is quasi-Frobenius. This settles a conjecture of W. V. Vasconcelos [2].

References [Enhancements On Off] (What's this?)

  • [1] H. Bass, On the ubiquity of Gorenstein rings, Math. Z. 83 (1963), 8-28. MR 27 #3669. MR 0153708 (27:3669)
  • [2] W. V. Vasconcelos, On commutative endomorphism rings, Pacific J. Math. 35 (1970), 795-798. MR 43 #4812. MR 0279086 (43:4812)

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Keywords: Endomorphism ring, isolated prime ideal, embedded prime ideal, total quotient ring, quasi-Frobenius ring, unmixed ideal
Article copyright: © Copyright 1973 American Mathematical Society

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