
Re: Basis of module and basis of vector space qs.
Posted:
Nov 19, 2013 10:53 AM


On Tuesday, November 19, 2013 7:59:57 AM UTC6, Sandy wrote: > Arturo Magidin wrote: > > > On Monday, November 18, 2013 2:17:05 PM UTC6, Sandy wrote: > > >> Is it the case that > > >> > > >> > > >> > > >> a module has a basis iff it is a free module? > > > > > > Yes. > > > > > > > > >> Is it the case that > > >> > > >> > > >> > > >> (i) every vector space has a basis iff the axiom of choice holds; > > > > > > Yes. > > > > > > > > >> (ii) for every vector space V, > > >> > > >> (if B and C are bases of V then, there is a bijection: B > C) > > > > " then," was probably meant to be ", then" :(. > > > > >> iff the axiom of choice holds > > > > > > I don't know for sure, but my dim memory is that this is strictly weaker than the full axiom of choice. You might want to check out the website/book on equivalents to the Axiom of Choice by the Rubins. > > > > Thank you. I know of the book but I don't have ready access to it, so I > > shall firtle around the Internet.
Try math.stackexchange.com; or perhaps mathoverlow.net

