An Introduction to Nonassociative Algebras

algebra over F algebraic closure algebras of characteristic alternative algebra QI Amer arbitrary field Artin associative algebra bimodule Cayley algebra central simple algebras central simple Jordan Corollary defined derivation of QI division algebra elements of QI equivalent F of characteristic field F finite finite-dimensional alternative algebra follows ideal of QI identity element implies inner derivation involution isomorphic Jacobson 25 Jordan identity L(QI Let QI linear operators Math multiplication algebra multiplications of QI nilalgebra nilideal nilpotent elements nonassociative algebras noncommutative Jordan algebra nondegenerate pairwise orthogonal idempotents Peirce decomposition power-associative algebra properly nilpotent prove QI contains QI is associative QI is called QI over F Qſil Qſo Qſoo R(QI ring scalar extension Similarly simple Jordan algebra simple Lie algebras space direct sum split Cayley algebra subalgebra of QI trace form unique unity element vector space direct Wedderburn x in QI