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  3. given the sub-ring a = z × z ? r 2 ,where, in r 2

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

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Advance Math

Given the sub-ring A = Z × Z ? R 2 ,Where, in R2 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 ofA.

d) Calculate A/U.

e) ¿It is U an ideal of R2?

I need all the paragraphs thanks

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