Simplicial affine semigroups with monomial minimal reduction ideals
Marco D'Anna, Raheleh Jafari, Francesco Strazzanti
TL;DR
This paper characterizes when the monomial maximal ideal of a simplicial affine semigroup ring has a monomial minimal reduction, and explores its algebraic properties and bounds related to the reduction number.
Contribution
It provides a characterization of monomial minimal reductions in simplicial affine semigroup rings and analyzes their Cohen-Macaulay and Gorenstein properties.
Findings
Characterization of when the monomial maximal ideal has a monomial minimal reduction
Analysis of Cohen-Macaulay and Gorenstein properties of the associated graded ring
Bounds for the reduction number with respect to the monomial minimal reduction
Abstract
We characterize when the monomial maximal ideal of a simplicial affine semigroup ring has a monomial minimal reduction. When this is the case, we study the Cohen-Macaulay and Gorenstein properties of the associated graded ring and provide several bounds for the reduction number with respect to the monomial minimal reduction.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models