September 29, 2025Open Access

Betti numbers and almost complete intersection monomial ideals

Key Points

An explicit formula for the Betti numbers of almost complete intersection monomial ideals is provided.
The construction of minimal free resolutions for these ideals is facilitated by the formula.
Cohen-Macaulayness for almost complete intersection monomial ideals is characterized effectively.
The paper also extends the findings to include dominant monomial ideals.

Abstract

Let R=Kx₁, , xₙ be the polynomial ring in n variables over a field K and let I be a monomial ideal of R. In this paper, we present an explicit formula for the Betti numbers of almost complete intersection monomial ideals, which enables a rapid construction of their minimal free resolutions. In addition, we characterize the Cohen-Macaulayness of these ideals and also we show the same result for dominant monomial ideals.

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Cite This Study

Мафи et al. (Sat,) studied this question.

synapsesocial.com/papers/68da58d8c1728099cfd111e4 https://doi.org/https://doi.org/10.48550/arxiv.2505.18788

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