Answer to Question #47348 in Abstract Algebra for ayush kumar

Question

(a) Show that the group G = {I, 3, 5, under multiplication modulo 8 is isomorphic to the group H = ri, 5, 7, T11 u nder multiplication modulo 12. Also show that neither of them is isomorphic to the group F= {I, 3, 7, 9} under multiplication modulo 10.

(b) Check whether Q [x](4x7 — 3x5+ 3x4 — 15) is a field or not. If it is a field, give its characteristic. If
it is not a field, obtain its quotient field.

(c) Let R and R' be commutative rings and f : R--->Rr be a ring homomorphism. If I is an
ideal of R, check whether f(I) is an deal of
R' or not.