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Proceedings of the American Mathematical Society

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

 

 

An ideal criterion for torsion freeness


Author: Mark Bridger
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
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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).


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DOI: https://doi.org/10.1090/S0002-9939-1972-0301001-7
Keywords: Syzygies, projective equivalence, finite projective dimension, fitting invariants, invariant factors, extension functors, regular sequences, k-torsion freeness, grade
Article copyright: © Copyright 1972 American Mathematical Society