Abstract
(1) f: R” + R” is a C” map. Here k is the real numbers R and R is the ring of C” maps from R” to R. (2) f: C” + C” is an analytic map. Here k is the complex numbers C and R is the ring of analytic maps from C” to C. (3) f: k” -+ k” is a polynomial map. Here k is a commutative ring and R is the polynomial ring kc”‘. (4) f:k[[I',k[[nll is a k-algebra homomorphism. Here k is a commutative ring and R is the formal power series ring kccnl’.
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