Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Annihilators of modules with a finite free resolution
HTML articles powered by AMS MathViewer

by Wolmer V. Vasconcelos PDF
Proc. Amer. Math. Soc. 29 (1971), 440-442 Request permission

Abstract:

Let A be a commutative ring and let E be an A-module with a finite free resolution (see below for definition). Extending results known previously for noetherian rings, it is shown that ${\text {ann}}(E)=\text {annihilator}$ of E is trivial if and only if the Euler characteristic of $E = \chi (E) > 0$; in addition, if $\chi (E) = 0,{\text {ann}}(E)$ is dense (i.e. ${\text {ann}}({\text {ann}}(E)) = 0$). Also, a local ring is constructed with its maximal ideal with a finite free resolution but consisting exclusively of zero-divisors and thus, contrary to the noetherian case, one does not always have a nonzero divisor in ${\text {ann}}(E)$ if $\chi (E) = 0$. Finally, if E has a finite resolution by (f.g.) projective modules it turns out that ${\text {ann}}({\text {ann}}(E))$ is generated by an idempotent element.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13.40
  • Retrieve articles in all journals with MSC: 13.40
Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 29 (1971), 440-442
  • MSC: Primary 13.40
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0280478-9
  • MathSciNet review: 0280478