Ulrich ideals of Gorenstein numerical semigroup rings with embedding dimension 3

Numata, Takahiro

doi:10.1216/jca-2017-9-1-143

Cited by 2 publications

(1 citation statement)

References 7 publications

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“…this new line of investigation, other works have appeared in the literature as for example [12], [14], [16], [27]. Now let us briefly comment on our main results, section by section.…”

Section: Introductionmentioning

confidence: 66%

On the theory of generalized Ulrich modules

Miranda-Neto¹,

S.²,

Souza³

2022

Preprint

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In this paper we further develop the theory of generalized Ulrich modules over Cohen-Macaulay local rings introduced in 2014 by Goto, Ozeki, Takahashi, Watanabe and Yoshida. The term generalized refers to the fact that Ulrich modules are taken with respect to a zero-dimensional ideal which is not necessarily the maximal ideal, the latter situation corresponding to the classical theory from the 80's; despite the apparent naivety of the idea, this passage adds considerable depth to the theory and enlarges its horizon of applications. First, we address the problem of when the Hom functor preserves the Ulrich property, and in particular we study relations with semidualizing modules. Second, we explore horizontal linkage of Ulrich modules, which we use to provide a characterization of Gorensteiness. Finally, we investigate connections between Ulrich modules and modules with minimal multiplicity, including characterizations in terms of relative reduction numbers as well as the Castelnuovo-Mumford regularity of certain blowup modules.

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“…this new line of investigation, other works have appeared in the literature as for example [12], [14], [16], [27]. Now let us briefly comment on our main results, section by section.…”

Section: Introductionmentioning

confidence: 66%

On the theory of generalized Ulrich modules

Miranda-Neto¹,

S.²,

Souza³

2022

Preprint

View full text Add to dashboard Cite

show abstract

On the theory of generalized Ulrich modules

Miranda-Neto

Souza

2023

Pacific J. Math.

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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 functor and horizontal linkage preserve the Ulrich property. One of the applications is a new characterization of quadratic hypersurface rings. Moreover, in the Gorenstein case, we deduce that applying linkage to sufficiently high syzygy modules of Ulrich ideals yields Ulrich modules. Finally, we explore connections to the theory of modules with minimal multiplicity, and as a byproduct we determine the Chern number of an Ulrich module as well as the Castelnuovo-Mumford regularity of its Rees module.

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Ulrich ideals of Gorenstein numerical semigroup rings with embedding dimension 3

Cited by 2 publications

References 7 publications

On the theory of generalized Ulrich modules

On the theory of generalized Ulrich modules

On the theory of generalized Ulrich modules

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