Modules with pure resolutions |
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Authors: | H Ananthnarayan Rajiv Kumar |
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Institution: | Department of Mathematics, I.I.T. Bombay, Powai, Mumbai, India |
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Abstract: | Let R a standard graded algebra over a field k. In this paper, we give a relation in terms of graded Betti numbers, called the Herzog–Kühl equations, for a pure R-module M to satisfy the condition dim(R)?depth(R) = dim(M)?depth(M). When R is Cohen–Macaulay, we prove an analogous result characterizing all graded Cohen–Macaulay R-modules of finite projective dimension. Finally, as an application, we show that the property of R being Cohen–Macaulay is characterized by the existence of pure Cohen–Macaulay R-modules corresponding to any degree sequence of length at most depth(R). |
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Keywords: | Cohen–Macaulay defect graded Betti numbers Herzog–Kühl equations pure modules |
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