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1.
In this paper, the strongly Cohen-Macaulay ideals of secondanalytic deviation one are characterized in terms of the depthproperties of the powers of the ideal in the standardrange. This provides an explanation of the behaviourof certain ideals that have appeared in the literature. 2000Mathematics Subject Classification 13H10 (primary), 13C40, 13D02,13D25 (secondary). 相似文献
2.
In this paper the asymptotic behavior of the Castelnuovo$ndash;Mumford regularity of powers of a homogeneous ideal I is studied. It is shown that there is a linear bound for the regularity of the powers I whose slope is the maximum degree of a homogeneous generator of I, and that the regularity of I is a linear function for large n. Similar results hold for the integral closures of the powers of I. On the other hand we give examples of ideal for which the regularity of the saturated powers is asymptotically not a linear function, not even a linear function with periodic coefficients. 相似文献
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Let I be a homogeneous ideal of a polynomial ring K[x1,…, xn] over a field K, and denote the Castelnuovo–Mumford regularity of I by reg(I). When I is a monomial complete intersection, it is proved that reg(Im) ≤ mreg(I) holds for any m ≥ 1. When n = 3, for any homogeneous ideals I and J of K[x1, x2, x3], one has that reg(I ? J), reg(IJ) and reg(I ∩ J) are all upper bounded by reg(I) +reg(J), while reg(I + J) ≤reg(I) +reg(J) ?1. 相似文献
5.
Mamoru Furuya 《代数通讯》2013,41(8):3130-3146
Let A be an analytic algebra over a field k of characteristic p > 0. In this article, for an analytic k-algebra we introduce the concept of analytic pn-basis which generalizes the pn-basis defined in [1], and the concept of an pn-admissible field for an algebraic function field, we give regularity criteria and absolute regularity criteria for an analytic algebra A/k in terms of the higher differential algebra and analytic pn-basis. The results are partial extension of our previous results for affine algebras to the case of analytic algebras (cf. [1, 3]), and these are partial generalization of results of Orbanz in the analytic case (cf. [9]). 相似文献
6.
The purpose of this short paper is to give a structure theorem for certain Gorenstein ideals. 相似文献
7.
Abhishek Banerjee 《代数通讯》2013,41(3):1067-1077
The object of this article is to study the regularity properties of elements of a ring with respect to a given ideal I. As expected, several concepts that are equivalent in the case of I = R turn out to be distinct for a general ideal I and we consider the relations between these properties. In particular, we replace the set of units U(R) of the ring R by the set U I (R) = {u|uI = Iu = I} and use these “relative units” to obtain generalizations of notions such as stable range and unit-regularity. We also see that on assuming the set of “relative units” to have no zero divisors, we can obtain several interesting results. 相似文献
8.
单项式理想是多项式环中一类重要的理想,这类理想的生成元和超图的边之间可以一一对应.超图的边理想的很多代数性质和它的组合性质之间有密切的联系.根据线图、圈图和单项式理想的正则度的一些公式,通过构造合适的短正合列,给出了两类m-剖分图的边理想的正则度的精确公式,分别推广了m个顶点的线图和圈图的正则度公式. 相似文献
9.
R. M. Aron P. Galindo D. Garcí a M. Maestre 《Transactions of the American Mathematical Society》1996,348(2):543-559
A Banach space is known to be Arens regular if every continuous linear mapping from to is weakly compact. Let be an open subset of , and let denote the algebra of analytic functions on which are bounded on bounded subsets of lying at a positive distance from the boundary of We endow with the usual Fréchet topology. denotes the set of continuous homomorphisms . We study the relation between the Arens regularity of the space and the structure of .
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We consider real analytic involutive structures 𝒱, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of 𝒱. We prove that analytic regularity propagates along them. With a further assumption on the level sets of 𝒱 we characterize the global analytic hypoellipticity of a differential operator naturally associated to 𝒱. As an application we study a case of tube structures. 相似文献
12.
Sarfraz Ahmad 《代数通讯》2013,41(2):670-673
We show that the regularity of monomial ideals of K[x 1,…, x n ] (K being a field), whose associated prime ideals are totally ordered by inclusion is upper bounded by a linear function in n. 相似文献
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Maria Vaz Pinto 《代数通讯》2013,41(9):3376-3396
Let X* be a subset of an affine space 𝔸 s , over a finite field K, which is parameterized by the edges of a clutter. Let X and Y be the images of X* under the maps x → [x] and x → [(x, 1)], respectively, where [x] and [(x, 1)] are points in the projective spaces ? s?1 and ? s , respectively. For certain clutters and for connected graphs, we were able to relate the algebraic invariants and properties of the vanishing ideals I(X) and I(Y). In a number of interesting cases, we compute its degree and regularity. For Hamiltonian bipartite graphs, we show the Eisenbud–Goto regularity conjecture. We give optimal bounds for the regularity when the graph is bipartite. It is shown that X* is an affine torus if and only if I(Y) is a complete intersection. We present some applications to coding theory and show some bounds for the minimum distance of parameterized linear codes for connected bipartite graphs. 相似文献
15.
Vijay Kodiyalam 《Proceedings of the American Mathematical Society》2000,128(2):407-411
Let be a polynomial ring over a field. For a graded -module generated in degree at most , the Castelnuovo-Mumford regularity of each of (i) its symmetric power, (ii) its torsion-free symmetric power and (iii) the integral closure of its torsion-free symmetric power is bounded above by a linear function in with leading coefficient at most . For a graded ideal of , the regularity of is given by a linear function of for all sufficiently large . The leading coefficient of this function is identified.
16.
This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.
17.
Maria Evelina Rossi Ngô Viê t Trung Giuseppe Valla 《Transactions of the American Mathematical Society》2003,355(5):1773-1786
Our main result shows that the Castelnuovo-Mumford regularity of the tangent cone of a local ring is effectively bounded by the dimension and any extended degree of . From this it follows that there are only a finite number of Hilbert-Samuel functions of local rings with given dimension and extended degree.
18.
Nordine Mir 《Journal of Geometric Analysis》2017,27(3):1920-1939
Let \(M\subset {\mathbb {C}}^N\) and \(M'\subset {\mathbb {C}}^{N'}\) be real-analytic CR submanifolds, with M minimal. We provide a new sufficient condition, that happens to be also essentially necessary, for all sufficiently smooth CR maps \(h:U\rightarrow M'\) defined on a connected open subset of M and of rank larger than a prescribed integer r to be real-analytic on a dense open subset of U. This condition corresponds to the nonexistence of nontrivial holomorphic deformations of germs of real-analytic CR mappings whose rank is larger than r. As a consequence, we obtain several new results about analyticity of CR mappings that, at the same time, generalize and unify a number of previous existing ones. 相似文献
19.
Isabel Bermejo Philippe Gimenez 《Proceedings of the American Mathematical Society》2000,128(5):1293-1299
We give an effective method to compute the regularity of a saturated ideal defining a projective curve that also determines in which step of a minimal graded free resolution of the regularity is attained.
20.
Kohji Yanagawa 《Journal of Pure and Applied Algebra》2006,207(1):77-97
Let A be a noetherian AS-regular Koszul quiver algebra (if A is commutative, it is essentially a polynomial ring), and the category of finitely generated graded left A-modules. Following Jørgensen, we define the Castelnuovo-Mumford regularity of a complex in terms of the local cohomologies or the minimal projective resolution of M•. Let A! be the quadratic dual ring of A. For the Koszul duality functor , we have . Using these concepts, we interpret results of Martinez-Villa and Zacharia concerning weakly Koszul modules (also called componentwise linear modules) over A!. As an application, refining a result of Herzog and Römer, we show that if J is a monomial ideal of an exterior algebra E=?〈y1,…,yd〉, d≥3, then the (d−2)nd syzygy of E/J is weakly Koszul. 相似文献