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On nilpotence and algebraicity in algebras over uncountable fields

Abstract

This thesis is primarily concerned with properties of nilpotence and algebraicity in algebras over fields. We study properties of certain non-commutative polynomials, which are called the order-symmetric polynomials. We give an alternative proof to Amitsur's theorem that algebraic algebras over uncountable fields have locally bounded degree. We also prove that the associated graded algebra of a filtered algebraic algebra over an uncountable field is nil

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