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.References
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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