Abstract
It is shown that a ring homomorphism on H(G), the algebra of analytic functions on a regular region G in the complex plane, is either linear or conjugate linear provided that the ring homomorphism takes the identity function into a nonconstant function.
Highlights
An operator M on a commutative algebra A is called a rlmg hoorphlsm if for all x,y e A, M(x+y) M(x) + M(y) and M(xy) M(x)M(y)
If N is a maximal ideal in H(G) the quotient algebra H(G)/N is isomorphic to C if and only if N is the kernel of a linear homomorphlsm
Thls implies that there exist discontinuous homomorphisms from the ring of entire functions onto C
Summary
Algebra of analytic function, Linear, Conjugate linear. 1980 AMS SUBJECT CLASSIFICATION CODE. 30H05
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