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arXiv · 2109.12918

The reduction number of stretched ideals

Kazuho Ozeki
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Abstract

The homological property of the associated graded ring of an ideal is an important problem in commutative algebra and algebraic geometry. In this paper we explore the almost Cohen-Macaulayness of the associated graded ring of stretched $\mathfrak{m}$-primary ideals in the case where the reduction number attains almost minimal value in a Cohen-Macaulay local ring $(A,\mathfrak{m})$. As an application, we present complete descriptions of the associated graded ring of stretched $\mathfrak{m}$-primary ideals with small reduction number.

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Kazuho Ozeki. 2021-09-27. The reduction number of stretched ideals. https://arxiv.org/abs/2109.12918

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