On the Frobenius functor and colon ideals
Wenliang Zhang
TL;DR
This paper investigates how the Frobenius functor interacts with colon ideals in Noetherian rings of positive characteristic, providing new characterizations of regular rings and local UFDs.
Contribution
It introduces novel characterizations of regular rings and local UFDs based on the behavior of the Frobenius functor with colon ideals.
Findings
Characterizations of regular rings via Frobenius and colon ideals
Characterizations of local UFDs using Frobenius functor properties
Insights into the commutativity of Frobenius and colon operations
Abstract
In this paper we study the commutativity of the Frobenius functor and the colon operation of two ideals for Noetherian rings of positive characteristic . New characterizations of regular rings and local UFDs are given.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models