共查询到20条相似文献,搜索用时 15 毫秒
1.
For an ideal generated by all square-free monomials of degree m in a polynomial ring R with n variables, we obtain a specific embedding of a canonical module of to itself. The construction of this explicit embedding depends on a minimal free R-resolution of an ideal generated by . Using this embedding, we give a resolution of connected sums of several copies of certain Artin -algebras where is a field. 相似文献
2.
Saeed Nasseh Sean Sather-Wagstaff Ryo Takahashi Keller VandeBogert 《Journal of Pure and Applied Algebra》2019,223(3):1272-1287
We construct a local Cohen–Macaulay ring R with a prime ideal such that R satisfies the uniform Auslander condition (UAC), but the localization does not satisfy Auslander's condition (AC). Given any positive integer n, we also construct a local Cohen–Macaulay ring R with a prime ideal such that R has exactly two non-isomorphic semidualizing modules, but the localization has non-isomorphic semidualizing modules. Each of these examples is constructed as a fiber product of two local rings over their common residue field. Additionally, we characterize the non-trivial Cohen–Macaulay fiber products of finite Cohen–Macaulay type. 相似文献
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Lukas Katthän 《Journal of Pure and Applied Algebra》2019,223(3):1227-1245
Let be a squarefree monomial ideal in a polynomial ring. In this paper we study multiplications on the minimal free resolution of . In particular, we characterize the possible vectors of total Betti numbers for such ideals which admit a differential graded algebra (DGA) structure on . We also show that under these assumptions the maximal shifts of the graded Betti numbers are subadditive.On the other hand, we present an example of a strongly generic monomial ideal which does not admit a DGA structure on its minimal free resolution. In particular, this demonstrates that the Hull resolution and the Lyubeznik resolution do not admit DGA structures in general.Finally, we show that it is enough to modify the last map of to ensure that it admits the structure of a DG algebra. 相似文献
4.
Sarah Mayes-Tang 《Journal of Pure and Applied Algebra》2019,223(2):571-579
Given an ideal I we investigate the decompositions of Betti diagrams of the graded family of ideals formed by taking powers of I. We prove conjectures of Engström from [5] and show that there is a stabilization in the Boij–Söderberg decompositions of for when I is a homogeneous ideal with generators in a single degree. In particular, the number of terms in the decompositions with positive coefficients remains constant for , the pure diagrams appearing in each decomposition have the same shape, and the coefficients of these diagrams are given by polynomials in k. We also show that a similar result holds for decompositions with arbitrary coefficients arising from other chains of pure diagrams. 相似文献
5.
Bhargav Bhatt 《Journal of Pure and Applied Algebra》2019,223(5):1940-1945
Given a commutative ring A and a finitely generated ideal I, we prove that -torsion A-modules that are also I-adically complete (or merely derived I-complete) must have bounded -torsion, i.e., they are killed by for some . 相似文献
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Let R be an affine domain of dimension over a field of characteristic 0 and . Let be a local complete intersection ideal of height n such that . This paper examines under what condition I is surjective image of a projective D-module of rank n. 相似文献
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In this note we describe the minimal resolution of the ideal , the saturation of the Jacobian ideal of a nearly free plane curve . In particular, it follows that this ideal can be generated by at most 4 polynomials. Related general results by Hassanzadeh and Simis on the saturation of codimension 2 ideals are discussed in detail. Some applications to rational cuspidal plane curves and to line arrangements are also given. 相似文献
8.
Federico Galetto Anthony V. Geramita Yong-Su Shin Adam Van Tuyl 《Journal of Pure and Applied Algebra》2019,223(6):2709-2731
Let I be a homogeneous ideal of . To compare , the m-th symbolic power of I, with , the regular m-th power, we introduce the m-th symbolic defect of I, denoted . Precisely, is the minimal number of generators of the R-module , or equivalently, the minimal number of generators one must add to to make . In this paper, we take the first step towards understanding the symbolic defect by considering the case that I is either the defining ideal of a star configuration or the ideal associated to a finite set of points in . We are specifically interested in identifying ideals I with . 相似文献
9.
Nursel Erey 《Journal of Pure and Applied Algebra》2019,223(7):3071-3080
Let G be a -free graph with edge ideal . We show that has linear resolution for every . Also, we show that every power of the vertex cover ideal of G has linear quotients. As a result, we describe the Castelnuovo–Mumford regularity of powers of in terms of the maximum degree of G. 相似文献
10.
Let R be a polynomial ring over a field and I an ideal generated by three forms of degree three. Motivated by Stillman's question, Engheta proved that the projective dimension of is at most 36, although the example with largest projective dimension he constructed has . Based on computational evidence, it had been conjectured that . In the present paper we prove this conjectured sharp bound. 相似文献
11.
Let R and S be standard graded algebras over a field k, and and homogeneous ideals. Denote by P the sum of the extensions of I and J to . We investigate several important homological invariants of powers of P based on the information about I and J, with focus on finding the exact formulas for these invariants. Our investigation exploits certain Tor vanishing property of natural inclusion maps between consecutive powers of I and J. As a consequence, we provide fairly complete information about the depth and regularity of powers of P given that R and S are polynomial rings and either or I and J are generated by monomials. 相似文献
12.
Let be a polynomial ring, where is a field, and G be a simple graph on n vertices. Let be the vertex cover ideal of G. Herzog, Hibi and Ohsugi have conjectured that all powers of vertex cover ideals of chordal graph are componentwise linear. Here we establish the conjecture for the special case of trees. We also show that if G is a unicyclic vertex decomposable graph, then symbolic powers of are componentwise linear. 相似文献
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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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Raymond C. Heitmann 《Journal of Pure and Applied Algebra》2022,226(1):106809
It is shown that if is a complete local domain with and is its integral closure in an algebraic closure of the quotient field, then both the -adic and p-adic completions of are integral domains. More generally, this theorem remains true if the completeness assumption is relaxed to allow R to be an analytically irreducible Henselian local ring. It is also shown that these rings, which are Cohen-Macaulay R-modules (even balanced in the -adic case), will have dimension larger than the dimension of R unless . 相似文献
20.
Let be the finite field of order q. Let G be one of the three groups , or and let W be the standard n-dimensional representation of G. For non-negative integers m and d we let denote the representation of G given by the direct sum of m vectors and d covectors. We exhibit a minimal set of homogeneous invariant polynomials such that for all cases except when and or . 相似文献