UC San Diego
On nilpotence and algebraicity in algebras over uncountable fields
- Author(s): Regev, Alon
- et al.
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