Example: bachelor of science
Hws Series
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1 Homework 1 - University of Pennsylvania
www2.math.upenn.edu(5) Let F be a field and F[[z]] the ring of power series. (a) Show that every element A= P ∞ i=0 a iz i such that a 0 6= 0 is a unit in F[[z]]. SOLUTION: We want to show that there is B= P ∞ i=0 b iz i such that AB= 1 + 0z+ 0z2 + ...The coefficient b 0 must therefore be a−1 0 which exists since a 0 is assumed to be a nonzero element in a ...