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Open Access Publications from the University of California

On nilpotence and algebraicity in algebras over uncountable fields


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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