Results 31 to 40 of about 34,885 (140)
Hilbert-Kunz density function for graded domains
, 2022 We prove the existence of HK density function for a graded pair (R,I), where R is an N-graded domain of finite type over a perfect field and I⊂R is a graded ideal of finite colength.
Trivedi, Vijaylaxmi, Watanabe, Kei-Ichi
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BMC Urology, 2018 Background The diagnostic pathway for prostate cancer (PCa) is advancing towards an imaging-driven approach. Multiparametric magnetic resonance imaging, although increasingly used, has not shown sufficient accuracy to replace biopsy for now.
Christophe K. Mannaerts +8 more
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Porcupine-quotient graphs, the fourth primary color, and graded composition series of Leavitt path algebras [PDF]
, 2023 If $E$ is a directed graph, $K$ is a field, and $I$ is a graded ideal of the Leavitt path algebra $L_K(E),$ $I$ is completely determined by an admissible pair $(H,S)$ of two sets of vertices of $E$.
Vas, Lia
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Journal of Algebra, 2000 Let \((A,m)\) be a Noetherian local ring with maximal ideal \(m\) and suppose that the residue field \(A/m\) is infinite. Let \(E\) be a finitely generated \(A\)-module of positive dimension \(s\). \textit{Y. Nakamura} [J. Algebra 209, 345-366 (1998; Zbl 0942.13002)] gave necessary and sufficient conditions for the associated graded rings of \(m ...
Shimoda, Yasuhiro, Yamagishi, Kikumichi
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On the Hilbert depth of the Hilbert function of a finitely generated graded module
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaLet K be a field, A a standard graded K-algebra and M a finitely generated graded A-module. Inspired by our previous works, see [2] and [3], we study the invariant called Hilbert depth of hM, that is hdepth(hM)=max{d:∑j≤k(-1)k-j(d-jk-j)hM(j)≥0 for all ...
Bălănescu Silviu, Cimpoeaş Mircea
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The Gorenstein property of the associated graded rings of powers of an ideal
, 1992 Let (R, m) be a local ring with d = dim(R)≥1 and with infinite residue field. By using Hilbert functions, we show the following theorem: Let I be an m-primary ideal such that the associated graded ring G(I) is Gorenstein.
Ooishi, Akira, Akira Ooishi
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The role of Diffusion Weighted MRI in Evaluation of Neoplastic Hepatic Focal Lesions in Cases of Portal Vein Thrombosis [PDF]
Al-Azhar International Medical JournalBackground: It is thought that many primary malignant, benign, and metastatic localized lesions share the liver as a location. In order to avoid inoperable tumors being falsely graded and cases with such tumors being scheduled for surgical treatments ...
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Depth of associated graded rings via Hilbert coefficients of ideals
, 2005 Given a local Cohen–Macaulay ring (R,m), we study the interplay between the integral closedness, or even the normality, of an m-primary R-ideal I and conditions on the Hilbert coefficients of I . We relate these properties to the depth of the associated
ROSSI, MARIA EVELINA, CORSO A, POLINI C
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Porcupine-quotient graphs, the fourth primary color, and graded composition series of Leavitt path algebras [PDF]
If E is a directed graph, K is a field, and I is a graded ideal of the Leavitt path algebra LK(E), then I is completely determined by a pair (H, S) of two sets of vertices of E, called an admissible pair, and one writes I = I(H, S) in this case.
Vaš, Lia
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On the Buchsbaum Property of Associated Graded Rings
, 1998 LetIbe an m-primary ideal in a Buchsbaum local ring (A,m). In this paper, we investigate the Buchsbaum property of the associated graded ring ofIwhen the equalityI2=qIholds for some minimal reduction q ofI. However, the Buchsbaum property does not always
Nakamura, Yukio
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