Talk:Identity Function is Completely Multiplicative

I posted this silly result up ages ago, and for the life of me I can't work out why I limited the domain to the positive integers. It occurs to me it holds for a considerably wider domain than that - trivially, up as far as $\C$ and beyond to $\Bbb H$ and even $\Bbb O$ and so on. Am I right or is lack of sleep doing silly things to my brain? --prime mover 03:17, 3 December 2011 (CST)

This correlates to the definition of a multiplicative function and the talk page there. I think one can generalise the definition of a completely multiplicative function, indeed up to stating it is a group (even magma maybe, but I'm not into magmas; the thing that is only closed under multiplication) homomorphism, but the results get scarcer because you lack things like unique factorisation... --Lord_Farin 03:22, 3 December 2011 (CST)