Given the sub-ring A = Z × Z ⊂ R 2 ,Where, in R 2 we...

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

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Expert Solution

Colby Messinger answered 1 year ago

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