Question: (Abstract Algebra - Rings and Ideals) Given: R = Z x Z (a) Show that I = {{x, y) R | x and y are

(Abstract Algebra - Rings and Ideals)

Given: R = Z x Z

(a) Show that I = {{x, y) R | x and y are even} is an ideal of R.

(b) Determine the elements of R/I.

(c) Is R/I an integral domain? Is R/I a field?

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