Question

Consider the set Q(√3) ={a+b√3| a,b∈Q}. We have the associative properties of usual addition and usual multiplication from the field of real number R.

a)Show that Q (√3) is closed under addition, contains the additive identity (0,zero) of R, each element contains the additive inverses, and say if addition is commutative. What does this tell you about (Q(√3,+)?

b) Prove that Q(√3) is a commutative ring with unity 1

c) Prove that Q(√3) is a field by showing every nonzero element is a unit.

Answer 1