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- W2893400900 abstract "We exhibit a class of Hibi rings which are diagonally F-regular over fields of positive characteristic, and diagonally $F$-regular type over fields of characteristic zero, in the sense of Carvajal-Rojas and Smolkin. It follows that such Hibi rings satisfy the uniform symbolic topology property effectively in all characteristics. Namely, for rings $R$ in this class of Hibi rings, we have $P^{(dn)} subseteq P^n$ for all $P in operatorname{Spec} R$, where $d = dim(R)$. Further, we demonstrate that all Hibi rings over fields of positive characteristic are 2-diagonally $F$-regular, and that the simplest Hibi ring not contained in the above class is not 3-diagonally $F$-regular in any characteristic. The former implies that $P^{(2d)} subseteq P^2$ for all $P in operatorname{Spec} R$." @default.
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- W2893400900 date "2018-09-29" @default.
- W2893400900 modified "2023-09-27" @default.
- W2893400900 title "Symbolic and Ordinary Powers of Ideals in Hibi Rings" @default.
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