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arXiv · 2004.06597

Properties of analogues of Frobenius powers of ideals

Subhajit Chanda·Arvind Kumar
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Abstract

Let $R=\mathbb{K}[X_1, \ldots , X_n ]$ be a polynomial ring over a field $\mathbb{K}$. We introduce an endomorphism $\mathcal{F}^{[m]}: R \rightarrow R $ and denote the image of an ideal $I$ of $R$ via this endomorphism as $I^{[m]}$ and call it to be the $m$ \textit{-th square power} of $I$. In this article, we study some homological invariants of $I^{[m]}$ such as regularity, projective dimension, associated primes and depth for some families of ideals e.g. monomial ideals.

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Subhajit Chanda, Arvind Kumar. 2020-04-14. Properties of analogues of Frobenius powers of ideals. https://arxiv.org/abs/2004.06597

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