Corrigendum to the paper “A remark on symbolic powers” (Studia Math. 249 (2019), 111–116)

2021 ◽  
Vol 258 (2) ◽  
pp. 239-239
Author(s):  
Alexander Rashkovskii
Keyword(s):  
Studia Math ◽  
Symbolic Powers

scholarly journals Wavelet Frames for Distributions in Anisotropic Besov Spaces

2005 ◽  
Vol 12 (4) ◽  
pp. 637-658
Author(s):  
Dorothee D. Haroske ◽  
Erika Tamási
Keyword(s):  
Large Class ◽  
Besov Spaces ◽  
Studia Math ◽  
Wavelet Frames ◽  
Anisotropic Besov Spaces ◽  
Wavelet Decompositions

Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎1, . . . , 𝑎𝑛) is an anisotropy, with 𝑎𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎1 + . . . + 𝑎𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [Triebel, Studia Math. 154: 59–88, 2003].

scholarly journals Symbolic Powers of Certain Cover Ideals of Graphs

2021 ◽  
Author(s):  
Arvind Kumar ◽  
Rajiv Kumar ◽  
Rajib Sarkar ◽  
S. Selvaraja
Keyword(s):  
Symbolic Powers

scholarly journals A Note on the $k$-Buchsbaum Property of Symbolic Powers of Stanley-Reisner Ideals

2011 ◽  
Vol 34 (1) ◽  
pp. 221-227 ◽  
Author(s):  
Nguyên Công MINH ◽  
Yukio NAKAMURA
Keyword(s):  
Symbolic Powers

scholarly journals Stanley depth and symbolic powers of monomial ideals

2017 ◽  
Vol 120 (1) ◽  
pp. 5 ◽  
Author(s):  
S. A. Seyed Fakhari
Keyword(s):  
Monomial Ideal ◽  
Monomial Ideals ◽  
Limit Behavior ◽  
Stanley Depth ◽  
Symbolic Powers

The aim of this paper is to study the Stanley depth of symbolic powers of a squarefree monomial ideal. We prove that for every squarefree monomial ideal $I$ and every pair of integers $k, s\geq 1$, the inequalities $\mathrm{sdepth} (S/I^{(ks)}) \leq \mathrm{sdepth} (S/I^{(s)})$ and $\mathrm{sdepth}(I^{(ks)}) \leq \mathrm{sdepth} (I^{(s)})$ hold. If moreover $I$ is unmixed of height $d$, then we show that for every integer $k\geq1$, $\mathrm{sdepth}(I^{(k+d)})\leq \mathrm{sdepth}(I^{{(k)}})$ and $\mathrm{sdepth}(S/I^{(k+d)})\leq \mathrm{sdepth}(S/I^{{(k)}})$. Finally, we consider the limit behavior of the Stanley depth of symbolic powers of a squarefree monomial ideal. We also introduce a method for comparing the Stanley depth of factors of monomial ideals.

scholarly journals Symbolic powers of cover ideals of graphs and Koszul property

2021 ◽  
pp. 1-17
Author(s):  
Yan Gu ◽  
Huy Tài Hà ◽  
Joseph W. Skelton
Keyword(s):  
Vertex Cover ◽  
Cycle Cover ◽  
Symbolic Powers ◽  
Koszul Property

We show that attaching a whisker (or a pendant) at the vertices of a cycle cover of a graph results in a new graph with the following property: all symbolic powers of its cover ideal are Koszul or, equivalently, componentwise linear. This extends previous work where the whiskers were added to all vertices or to the vertices of a vertex cover of the graph.

Symbolic Powers of Regular Primes

1981 ◽  
Vol 33 (6) ◽  
pp. 1331-1337 ◽  
Author(s):  
Yasunori Ishibashi
Keyword(s):  
Prime Ideal ◽  
Finite Type ◽  
Polynomial Ring ◽  
Type A ◽  
Symbolic Power ◽  
Perfect Field ◽  
Symbolic Powers ◽  
Higher Derivatives ◽  
Differential Filtration ◽  
Derivatives Of

In a recent paper [6], P. Seibt has obtained the following result: Let k be a field of characteristic 0, k[T1, … , Tr] the polynomial ring in r indeterminates over k, and let P be a prime ideal of k[T1, … , Tr]. Then a polynomial F belongs to the n-th symbolic power P(n) of P if and only if all higher derivatives of F from the 0-th up to the (n – l)-st order belong to P.In this work we shall naturally generalize this result so as to be valid for primes of the polynomial ring over a perfect field k. Actually, we shall get a generalization as a corollary to a theorem which asserts: For regular primes P in a k-algebra R of finite type, a certain differential filtration of R associated with P coincides with the symbolic power filtration (P(n))n≧0.

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