论文标题
Frobenius理想能力的类似物的特性
Properties of analogues of Frobenius powers of ideals
论文作者
论文摘要
令$ r = \ mathbb {k} [x_1，\ ldots，x_n] $是字段上的多项式环$ \ mathbb {k} $。我们介绍了一个内态$ \ Mathcal {f}^{[m]}：r \ rightArrow r $，并通过此内态形态为$ i^{[m]} $表示理想$ i $ of $ r $的图像，并称其为$ m $ m $ \ textIt textit fextit fextit {-th-thth square power} $ i $ i $ i $ i $ i $ i $ i $。在本文中，我们研究了$ i^{[m]} $的一些同源性不变性，例如规律性，投影维度，相关的素数和深度，例如某些理想家庭，例如单一理想。
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.
