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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Regularity conditions in nonnoetherian rings
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by T. Kabele PDF
Trans. Amer. Math. Soc. 155 (1971), 363-374 Request permission

Abstract:

We show that properties of $R$-sequences and the Koszul complex which hold for noetherian local rings do not hold for nonnoetherian local rings. For example, we construct a local ring with finitely generated maximal ideal such that ${\text {hd} _R}M < \infty$ but $M$ is not generated by an $R$-sequence. In fact, every element of $M - {M^2}$ is a zero divisor. Generalizing a result of Dieudonné, we show that even in local (nonnoetherian) integral domains a permutation of an $R$-sequence is not necessarily an $R$-sequence.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 155 (1971), 363-374
  • MSC: Primary 13.95
  • DOI: https://doi.org/10.1090/S0002-9947-1971-0274439-8
  • MathSciNet review: 0274439