On rings of analytic functions

Let D be a domain in the complex plane (Riemann sphere) and R(D) the totality of one-valued regular analytic functions defined in D. With the usual definitions of addition and multiplication R(D) becomes a commutative ring (in fact, a domain of integrity). A oneto-one conformai transformation f =0(z) of D onto a domain A induces an isomorphism ƒ—>ƒ* between R(D) and R(A):f(z) =ƒ*[</>(2)]. An anti-conformal transformation