Talk:Nonassociative ring

Cayley–Dickson[edit]

The statement The Cayley–Dickson construction provides an infinite family of nonassociative rings seems incorrect. Is there a reference? Deltahedron (talk) 17:59, 9 February 2014 (UTC)[reply]

The main references in Cayley-Dickson construction are Albert and Guy Roos. Reading that article it follows that if A is an algebra with involution, then B = A⊕A is another. The assertion about an infinite family refers to this process from A to B being repeated over and over.Rgdboer (talk) 22:30, 9 February 2014 (UTC)[reply]

Ah yes, of course: I think that needs to be made a little more explicit in this article. Incidentally, another infinite family of non-associative rings is given by the free non-associative algebras on an ascending sequence of sets of generators: I'm drafting something on that construction right now. Deltahedron (talk) 22:39, 9 February 2014 (UTC)[reply]