Timeline for Other Ring Structures on $\mathbb{Q}$

6 events

when toggle format	what		by	license	comment
Sep 1, 2011 at 10:42	comment	added	Emil Jeřábek		Yes, any bijection will do, it does not have to be linear, but I gather you learned this meanwhile from AKG’s answer.
Aug 31, 2011 at 18:55	comment	added	Aeryk		@Emil: I think this gives me some good insight. True or False: Any linear map $x \to ax+b$ will induce corresponding operations under which 1) $\mathbb{Q}$ is a ring and 2) the linear map gives the isomorphism with the standard operations? I would conjecture now that this is true.
Aug 31, 2011 at 18:54	comment	added	Pace Nielsen		True. But that seems to me to be just about as difficult (although it does give an idea of where it comes from).
Aug 31, 2011 at 18:48	comment	added	Emil Jeřábek		You don’t need to show any laws, just observe that $x\mapsto 1-x$ is an isomorphism of your structure with the usual $(\mathbb Q,+,\cdot)$.
Aug 31, 2011 at 18:44	history	edited	Pace Nielsen	CC BY-SA 3.0	added 1 characters in body
Aug 31, 2011 at 18:38	history	answered	Pace Nielsen	CC BY-SA 3.0