Recent content by dreamer.ande

Could you show me how to do it for the first part and I try out the second part? Sorry, I am new to this thing. Very Confusing for me.

how many axiom do i need to show to prove that it is a subring of a ring? There are five axiom to show? How to show that first axiom : containment. R belong to Z? Can you show me the proper step of proving in such question as I always have problem in such question?

that the part i am struck with. a+b\sqrt{2} + c+d\sqrt{2} ? but \sqrt{2} not an integer

I am lost totally in this question. I know i need to do this. need to show it is closed under addition, multiplication containing identity to prove it is a subring and show that it is surjective and injective. to show that it is isomorphism. Can you help me out in this question?

3. Let R = a+b \sqrt{2} , a,b is integer and let R_{2} consist of all 2 x 2 matrices of the form [\begin{array}{cc} a & 2b \\ b & a \\ \end{array} }] Show that R is a subring of Z(integer) and R_{2} is a subring of M_{2} (Z). Also. Prove that the mapping from R to R_{2} is a isomorphism.