Abstract Algebra Answers

Give an example of infinite ring of characteristic 2

Let G be the set of positive real numbers except 1. Define α∗β = α^lnβ. Then:

(a) show that (G,∗) is a group.

(b) Is G abelian? if not, find its center.

(c) Give an automorphism of G. 

Let G be the set of positive real numbers except 1. Define α∗β = α^nβ. Then:

(a) show that (G,∗) is a group.

(b) Is G abelian? if not, find its center.

(c) Give an automorphism of G. 

Let G=fg:R--li:g(x)=ax+b,a,b EQ,a# 01. Check whether or not G is a group with respect to the composition of mappings. For f(x) = 2x + 3, find all g bilong toG such that fog=gof

Any two non-zero subgroups of Z are isomorphic. 

4. Find Φ12(x) over Q.

Find all the zero divisors of 15.