On graded characterizations of finite dimensionality for algebraic\n algebras

2017/06/07 by Edward S. Letzter, Letzter, Edward S.
Mathematics · #16N40 #16U99 #16W70 #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1706.02383

openalex publication_date 2017/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We observe that a finitely generated algebraic algebra R (over a field) is\nfinite dimensional if and only if the associated graded ring grR is right\nnoetherian, if and only if grR has right Krull dimension, if and only if grR\nsatisfies a polynomial identity.\n

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