On reduction numbers and Castelnuovo–Mumford regularity of blowup rings and modules
CB Miranda-Neto, DS Queiroz - Collectanea Mathematica, 2024 - Springer
We prove new results on the interplay between reduction numbers and the Castelnuovo–
Mumford regularity of blowup algebras and blowup modules, the key basic tool being the …
Mumford regularity of blowup algebras and blowup modules, the key basic tool being the …
The structure of chains of Ulrich ideals in Cohen-Macaulay local rings of dimension one
S Goto, R Isobe, S Kumashiro - Acta Mathematica Vietnamica, 2019 - Springer
This paper studies Ulrich ideals in one-dimensional Cohen-Macaulay local rings. A
correspondence between Ulrich ideals and overrings is given. Using the correspondence …
correspondence between Ulrich ideals and overrings is given. Using the correspondence …
Residually faithful modules and the Cohen–Macaulay type of idealizations
S Goto, S Kumashiro, NTH Loan - Journal of the Mathematical …, 2019 - jstage.jst.go.jp
The Cohen–Macaulay type of idealizations of maximal Cohen–Macaulay modules over
Cohen–Macaulay local rings is closely explored. There are two extremal cases, one of …
Cohen–Macaulay local rings is closely explored. There are two extremal cases, one of …
[HTML][HTML] Ulrich modules over cyclic quotient surface singularities
Y Nakajima, K Yoshida - Journal of Algebra, 2017 - Elsevier
In this paper, we characterize Ulrich modules over cyclic quotient surface singularities using
the notion of special Cohen–Macaulay modules. We also investigate the number of …
the notion of special Cohen–Macaulay modules. We also investigate the number of …
Generalized Gorenstein Arf rings
E Celikbas, O Celikbas, S Goto, N Taniguchi - 2019 - projecteuclid.org
In this paper we study generalized Gorenstein Arf rings: a class of one-dimensional Cohen–
Macaulay local Arf rings that is strictly contained in the class of Gorenstein rings. We obtain …
Macaulay local Arf rings that is strictly contained in the class of Gorenstein rings. We obtain …
On a generalization of Ulrich modules and its applications
E Celikbas, O Celikbas, J Lyle, R Takahashi… - arXiv preprint arXiv …, 2023 - arxiv.org
We study a modified version of the classical Ulrich modules, which we call $ c $-Ulrich.
Unlike the traditional setting, $ c $-Ulrich modules always exist. We prove that these …
Unlike the traditional setting, $ c $-Ulrich modules always exist. We prove that these …
Characterization of generalized Gorenstein rings
S Goto, R Isobe, S Kumashiro, N Taniguchi - arXiv preprint arXiv …, 2017 - arxiv.org
arXiv:1704.08901v1 [math.AC] 28 Apr 2017 Page 1 arXiv:1704.08901v1 [math.AC] 28 Apr 2017
CHARACTERIZATION OF GENERALIZED GORENSTEIN RINGS SHIRO GOTO, RYOTARO …
CHARACTERIZATION OF GENERALIZED GORENSTEIN RINGS SHIRO GOTO, RYOTARO …
On the theory of generalized Ulrich modules
CB Miranda-Neto, DS Queiroz, TS Souza - Pacific Journal of Mathematics, 2023 - msp.org
We further develop the theory of generalized Ulrich modules introduced in 2014 by Goto et
al. Our main goal is to address the problem as to when the operations of taking the Hom …
al. Our main goal is to address the problem as to when the operations of taking the Hom …
Some Categorical Aspects of Commutative Algebra
S Dey - 2023 - search.proquest.com
The purpose of this work is to study commutative Noetherian rings by studying certain
subcategories of the category of finitely generated modules over such rings. We begin by …
subcategories of the category of finitely generated modules over such rings. We begin by …
The structure of Ulrich ideals in hypersurfaces
R Isobe - Journal of Pure and Applied Algebra, 2021 - Elsevier
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