In: Advanced Math
Given the sub-ring A = Z × Z ⊂ R 2 ,Where, in R 2 we have the sum operation and the complex product.
a) Prove that indeed A it is a sub-ring.
b) ¿It is A an entire domain?
c)Consider U = {(0, n) : n ∈ Z}, prove that U is an ideal of A.
d) Calculate A/U.
e) ¿It is U an ideal of R2?
I need all the paragraphs thanks