Graded annihilators and uniformly F-compatible ideals

2014/09/08 by Rodney Y. Sharp, Sharp, Rodney Y.
Mathematics · #13A35 #16S36 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13A35 #msc:16S36

paper · pdf · doi:10.48550/arxiv.1409.2319

17 pages. This paper has been accepted for publication in Acta Mathematica Vietnamica

arxiv created 2014/09/08 · openalex publication_date 2014/09/08 · arxiv updated 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a commutative (Noetherian) local ring of prime characteristic p that is F-pure. This paper is concerned with comparison of three finite sets of radical ideals of R, one of which is only defined in the case when R is F-finite (that is, is finitely generated when viewed as a module over itself via the Frobenius homomorphism). Two of the afore-mentioned three sets have links to tight closure, via test ideals. Among the aims of the paper are a proof that two of the sets are equal, and a proposal for a generalization of I. M. Aberbach's and F. Enescu's splitting prime.

Related

• Graded annihilators and tight closure test ideals
• Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure
• An excellent F-pure ring of prime characteristic has a big tight closure test element
• Tight closure with respect to a multiplicatively closed subset of an F-pure local ring
• Uniform Behaviour of the Frobenius closures of ideals generated by regular sequences