The monomial curves associated with balanced semigroups are set-theoretic complete intersections

Eto, Kazufumi

doi:10.1016/j.jalgebra.2007.08.016

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The Set Theoretic Complete Intersection Conjecture1

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Cited by 6 publications

(1 citation statement)

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“…These results were subsequently generalized by Thoma [55]. Eto [17] proved the conjecture when the integers define a balanced semigroup in dimension 4.…”

Section: The Set Theoretic Complete Intersection Conjecturementioning

confidence: 91%

Affine monomial curves

Sengupta¹

2020

Preprint

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“…These results were subsequently generalized by Thoma [55]. Eto [17] proved the conjecture when the integers define a balanced semigroup in dimension 4.…”

Section: The Set Theoretic Complete Intersection Conjecturementioning

confidence: 91%

Affine monomial curves

Sengupta¹

2020

Preprint

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On the algebraic invariants of certain affine semigroup rings

Prakash

Sengupta

2022

Semigroup Forum

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For a reduced one-dimensional complete local k-algebra R, Huneke et al. (Res. Math. Sci., 8(4), paper no. 60, 2021) introduced an important invariant, the reduced type. In this article, we study the extremal behavior of reduced type of some special numerical semigroup rings. For a numerical semigroup ring, the behavior of reduced type can be studied by analyzing the set of pseudo-Frobenius elements of the numerical semigroup. We give complete descriptions of pseudo-Frobenius elements of Bresinsky's numerical semigroups and duplication of numerical semigroups. Further, we explore the extremal behavior of reduced type for the associated semigroup rings.

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Affine monomial curves

Sengupta

2022

Proc Math Sci

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The monomial curves associated with balanced semigroups are set-theoretic complete intersections

Abstract: We call a semigroup in the set of non-negative integers minimally generated by n 1 , n 2 , n 3 , n 4 with n 1 + n 4 = n 2 + n 3 a balanced semigroup. We prove that the monomial curves associated with balanced semigroups are set-theoretic complete intersections.

Cited by 6 publications

References 10 publications

Affine monomial curves

Affine monomial curves

On the algebraic invariants of certain affine semigroup rings

Affine monomial curves

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