Central simple algebras with involution of the first kind. (Q558370)

This paper gives ingenious elementary proofs of various (mostly classical) results on central simple algebras, in particular of Albert's theorems asserting that (1)~every central simple algebra of exponent~2 has an involution of the first kind, i.e., a linear anti-automorphism of period~2, and that (2)~every central simple algebra of exponent~2 and degree~4 is a tensor product of two quaternion algebras. In a few extra lines, the arguments also yield Kneser's theorem on the extension of involutions of the first kind from a simple subalgebra. No assumption is made on the characteristic.