[seqfan] Please name this function.

[Ed Jeffery]

I know this is the wrong place to ask the following, so I apologize, but I
have been searching for many days and cannot find the answer:

What is the name of a function that is both additive and multiplicative but
not arithmetic (in the sense that x and y are usually not integers), such
that

f(x+y) = f(x)+f(y)

and

f(x*y) = f(x)*f(y)?

Thanks in advance.

LEJ