Predicting syzygies over monomial relations algebras |
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Authors: | Birge Zimmermann Huisgen |
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Institution: | 1. Department of Mathematics, University of Utah, 84112, Salt Lake City, Utah, USA
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Abstract: | We show that all projective resolutions over a monomial relations algebra Λ simplify drastically at the stage of the second
syzygy; more precisely, we show that the kernel of any homomorphism between two projective left Λ-modules is isomorphic to
a direct sum of principal left ideals generated by paths. As consequences, we obtain:
(a) |
a tight approximation of the finitistic dimensions of Λ in terms of the (very accessible) projective dimensions of the principal
left ideals generated by paths;
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(b) |
a basis for comparison of the ‘big’ and ‘little’ finitistic dimensions of Λ, yielding in particular that these two invariants
cannot differ by more than 1 and that they are equal in ‘most’ cases;
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(c) |
manageable algorithms for computation of finitistic dimensions.
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This research was partially supported by a grant from the National Science Foundation. |
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Keywords: | |
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