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Let be a Noetherian local ring and M a finitely generated R-module. The invariants and of M were introduced in [3] and [17] in order to measure the non-Cohen–Macaulayness and the non-sequential-Cohen–Macaulayness of M, respectively. Let be the filtration of M such that is the largest submodule of M of dimension less than for all and . In this paper we prove that if , then there exists a constant c such that for all good parameter ideals of M with respect to this filtration. Here is the reducibility index of on M. This is an extension of the main results of [19], [20], [24]. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(4):106890
A commutative Noetherian ring R is said to be Tor-persistent if, for any finitely generated R-module M, the vanishing of for implies M has finite projective dimension. An open question of Avramov, et al. asks whether any such R is Tor-persistent. In this work, we exploit properties of exterior powers of modules and complexes to provide several partial answers to this question; in particular, we show that every local ring with is Tor-persistent. As a consequence of our methods, we provide a new proof of the Tachikawa Conjecture for positively graded rings over a field of characteristic different from 2. 相似文献
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For an affine algebraic variety X we study a category of modules that admit compatible actions of both the algebra A of functions on X and the Lie algebra of vector fields on X. In particular, for the case when X is the sphere , we construct a set of simple modules that are finitely generated over A. In addition, we prove that the monoidal category that these modules generate is equivalent to the category of finite-dimensional rational -modules. 相似文献