----- 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?

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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