Answer to Question #47344 in Abstract Algebra for ayush kumar

Question

(a) Show that f : (R 4 , x) -4 (R, +), defined by f (a) = log10a, is an isomorphism of groups, where R+ is the set of positive real numbers.

(b)Give an example of a ring R such that a2 = a for all aER. Show that any such ring is commutative.

(c)Let (C*,.) denote the group of non-zero 3 complex numbers and let S = {zecx I IzI =1}
Show that C*/S~_ R+, where (R+,) is the group of positive real numbers.