Beyond simple counter examples to general statements, the Tarski school also pursued conditions on particular monoids which might imply uniqueness of a ring structure, or a definite range of ring structures. As I suggested, that open problem takes on a deeper significance if we consider it within categories of cohesion, not just within the category of abstract sets. Best wishes to all. Bill ************************************************************ On Fri, 11 Aug 2006, George Janelidze wrote:
FW: categories: Re: Linear--structure or property?Dear Florian,
1*2 = f(f(1)+f(2)) = f(1+3) = f(4) = f(2x2) = f(2)xf(2) = 3x3 = 9.
You are right, and thank you the correction (I think I thought of 3*3 = f(f(3)+f(3)) = f(2+2) =..., but does not matter of course).
Dear Bill,
Having two structures in {0,1} (with 1+1 = 0 and with 1+1 = 1) makes what you say about the Tarski school funny (sorry!)
Best regards to all-
George