Thread: Sum and Product of Functions

On PlanetMath.Org regarding the Sum and Product of Functions we find the following:

Let A be a set and K a field or skew field. If f: A K and g:A K, then one can define the product of functions f and g as the function fg: A K as follows:

(fg)(x) := f(x) . g(x) for all x belonging to A


My question is: Why cannot K be a group or a ring with . being the product concerned. Why does K have to be a field or a skew field?

Bernhard

Originally Posted by Bernhard

My question is: Why cannot K be a group or a ring with . being the product concerned. Why does K have to be a field or a skew field?

More general, we only need a binary operation i.e. for all , . So we can define in the way .