----- Original Message ---- From: Dan Asimov <dasimov@earthlink.net> To: Eugene Salamin <gene_salamin@yahoo.com> Sent: Tuesday, October 14, 2008 3:42:36 PM Subject: To Gene Re: [math-fun] what's the best way of finding n unknown integers from their sums taken k at a time Gene, Thanks for the correction (but I beat ya to it). << There are lots of infinite dimensional fields over the real or complex numbers, but what about infinite dimensional noncommutative or nonassociative division algebras? What is known about such creatures?
Years ago when Conway was active here, he stated that there are no infinite-dimensional real division algebras, unless I'm remembering wrong. That would seem to rule out complex ones as well, would you agree? --Dan ________________________________ Well there are lots of infinite dimensional fields, e.g. function fields, F extended by one or more transcendentals. Are you you saying that there is a Wedderburn type theorem here, that all infinite dimensional (real or complex) division algebras are fields? Is there such an animal as a free division algebra? Gene