arXiv subjects

Taiga Ozaki

Publications and source records attributed to Taiga Ozaki.

2 recordsLinked to original sources

arXiv2026

Higher-dimensional Teter rings via the canonical trace

We study Puthenpurakal's higher-dimensional Teter rings via the canonical trace ideal. We give a sufficient criterion for Teterness and show that, in the standard graded case, it is also necessary, yielding a characterization. Consequently, several nearly Gorenstein families are Teter; moreover, under certain hypotheses, the Cohen--Macaulay type of nearly Gorenstein rings is bounded by the codimension. We also analyze Teterness for fiber products, Veronese subrings, and numerical semigroup rings.

math.AC↗

arXiv2025

Pseudo-Frobenius numbers and defining ideals in stretched numerical semigroup rings

The pseudo-Frobenius numbers of a numerical semigroup $H$ are deeply connected to the structure of the defining ideal of its semigroup ring $k[H]$. In this paper, we resolve a certain conjecture related to this connection under the assumption that $k[H]/(t^a)$ is stretched, where $a$ is the multiplicity of $H$. Furthermore, we provide numerical conditions for the tangent cone of $k[H]$ to be Cohen-Macaulay.

math.AC↗