(a) Prove that Q(sqareroot 5)={a+b sqareroot 5 ; a,b in Z} is a subring of Z....

(a) Prove that Q(sqareroot 5)={a+b sqareroot 5 ; a,b in Z} is a subring of Z.

(b) Show that Q(sqareroot 5) is a conmutative ring.

(c) Show that Q(sqareroot 5) has a multiplicative identity.

(d) show that Q(sqareroot 5) is a field.(Hint : you want to mulitply something by he conjugate.)

(Abstract Algebra)

Expert Solution

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Colby Messinger answered 2 years ago

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Question

(a) Prove that Q(sqareroot 5)={a+b sqareroot 5 ; a,b in Z} is a subring of Z....

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