An ideal criterion for torsion freeness
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- by Mark Bridger PDF
- Proc. Amer. Math. Soc. 33 (1972), 285-291 Request permission
Abstract:
Auslander and Bridger have shown that, under conditions somewhat weaker than finite projective dimension, the “torsion freeness” properties of a module M (e.g. being reflexive, being the kth syzygy of another module) are determined by certain arithmetic conditions on the ${\text {Ext}^i}(M,R)$. In this paper it is shown that a single ideal, the intersection of the annihilators of these modules, gives this same information. This ideal is then related to the Fitting invariants and invariant factors of M, and a computation is made of certain syzygies of a quotient of M (by a regular M-sequence).References
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- Maurice Auslander and Mark Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, R.I., 1969. MR 0269685 D. Buchsbaum, Complexes associated with the minors of a matrix, Brandeis University, Waltham, Mass. (mimeographed notes).
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 285-291
- MSC: Primary 13C10; Secondary 16A64
- DOI: https://doi.org/10.1090/S0002-9939-1972-0301001-7
- MathSciNet review: 0301001