Constructing (almost) rigid rings and a UFD having infinitely generated Derksen and Makar-Limanov invariant

2007/06/28 by David R. Finston, Finston, David, Stefan Maubach +1 · 1 citation
Computer Science · Mathematics · #13A50 #13N15. #14R20 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.0706.4184

openalex publication_date 2007/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An example is given of a UFD which has infinitely generated Derksen invariant. The ring is \textquotedblleft almost rigid\textquotedblright meaning that the Derksen invariant is equal to the Makar-Limanov invariant. Techniques to show that a ring is (almost) rigid are discussed, among which is a generalization of Mason's abc-theorem.

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