Properties of analogues of Frobenius powers of ideals

2020/04/14 by Subhajit Chanda, Arvind Kumar, Chanda, Subhajit +1
Computer Science · Mathematics · #13A35 #13D02 #13F55 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13A35 #msc:13D02 #msc:13F55

paper · pdf · doi:10.48550/arxiv.2004.06597

9 pages

openalex publication_date 2020/04/14 · arxiv created 2020/08/01 · arxiv updated 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R=\mathbbK[X₁, … , X_n ] be a polynomial ring over a field \mathbbK. We introduce an endomorphism F^[m]: R → R and denote the image of an ideal I of R via this endomorphism as I^[m] and call it to be the m -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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• Frobenius powers
• Frobenius powers of some monomial ideals
• The Frobenius endomorphism and homological dimensions
• The resolution of the bracket powers of the maximal ideal in a diagonal hypersurface ring
• On the Stanley depth of powers of monomial ideals