On graded characterizations of finite dimensionality for algebraic algebras
classification
🧮 math.RA
keywords
onlyalgebraicfinitegradedrightalgebraalgebrasassociated
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We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring grR is right noetherian, if and only if grR has right Krull dimension, if and only if grR satisfies a polynomial identity.
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