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I-Chiau Huang

Publications and source records attributed to I-Chiau Huang.

8 recordsLinked to original sources
arXiv2026

Solution Module and Linear Closure

We introduce the notion of an ``initial condition'' for a module over a commutative Noetherian local ring, allowing for a recursive construction of its ``solution modules''. If the given module has zero-dimensional support, such as the residue field of the local ring and those encountered in residual complexes, we demonstrate that the solution module is an injective hull of the given module. The construction of the solution module for finitely generated given module is explicit and computable, devoid of the need for Zorn's lemma.

math.AC↗
arXiv2024

Affine Semigroup Algebras And Their Fibered Sums

We study affine semigroup rings as algebras over subsemigroup rings. From this relative viewpoint with respect to a given subsemigroup ring, the fibered sum of two affine semigroup algebras is constructed. Such a construction is compared to the tensor product and to the classical gluings of affine semigroup rings as defined in Rosales (1997). While fibered sum can always be achieved, gluings of affine semigroup rings do not always exist. Therefore, we further investigate when the fibered sum of affine semigroup algebras gives rise to a gluing. A criterion is recovered in terms of the defining semigroups under which the gluing may take place.

math.AC↗
arXiv2021

Coefficient Rings of Numerical Semigroup Algebras

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show that arithmetic and set-theoretic properties of a numerical semigroup ring are properties of an equi-gcd numerical semigroup algebra.

math.AC↗
arXiv2018

Factorizations in Numerical Semigroup Algebras

We study a numerical semigroup ring as an algebra over another numerical semigroup ring. The complete intersection property of numerical semigroup algebras is investigated using factorizations of monomials into minimal ones. The goal is to study whether a flat rectangular algebra is a complete intersection. Along this direction, special types of algebras generated by few monomials are worked out in detail.

math.AC↗
arXiv2006

Module structure of an injective resolution

Let A be the ring obtained by localizing the polynomial ring k[X,Y,Z,W] over a field k at the maximal ideal (X,Y,Z,W) and modulo the ideal (XW-YZ). Let p be the ideal of A generated by X and Y. We study the module structure of a minimal injective resolution of A/p in details using local cohomology. Applications include the description of Ext^i(M,A/p), where M is a module constructed by Dutta, Hochster and McLaughlin, and the Yoneda product of Ext^*(A/p,A/p).

math.AC↗