Regularity and intersections of bracket powers

2020/07/24 by Epstein, Neil
#13H05 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13A35 #Secondary: 13B40

paper · doi:10.48550/arxiv.2007.12738

Abstract

Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely one where finite intersection of ideals commutes with taking bracket powers. However, reducedness is essential for this equivalence. Connections are made with Ohm-Rush content theory, intersection-flatness of the Frobenius map, and various flatness criteria.

Related

• Test elements, excellent rings, and content functions
• A remark on regularity of powers and products of ideals
• Uniform Behaviour of the Frobenius closures of ideals generated by regular sequences
• Trace ideals, normalization chains, and endomorphism rings
• Ideal containment vs. powers