Question 6. [3+3+2+2 = 10 marks] Given the rings A = A, +, > with A...

  

Transcribed Image Text:

Question 6. [3+3+2+2 = 10 marks] Given the rings A = A, +, > with A = {a+b√2: a,b € Q}, and B = B, +, with B = {a+b√5: a,b € Q}. (a) Prove that the mapping 0: A → B defined by 0(a+b√2)= a +b√5 is not an isomorphism. (b) Show that the trinomial equation x² - 2ax + (a²-26²) = 0 has solutions in ring A for a, b € Q. (c) Write down a trinomial equation that has solutions in ring B. (d) Provide a reason why A & B. Question 6. [3+3+2+2 = 10 marks] Given the rings A = A, +, > with A = {a+b√2: a,b € Q}, and B = B, +, with B = {a+b√5: a,b € Q}. (a) Prove that the mapping 0: A → B defined by 0(a+b√2)= a +b√5 is not an isomorphism. (b) Show that the trinomial equation x² - 2ax + (a²-26²) = 0 has solutions in ring A for a, b € Q. (c) Write down a trinomial equation that has solutions in ring B. (d) Provide a reason why A & B.

Answer rating: 100% (QA)

a0 a bv2 a bv5 is not an isomorphism To prove this we need to show that there is no isomorphism betw... View the full answer