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  3. let r and s be nontrivial rings (i.e., containing

Let R and S be nontrivial rings (i.e., containing more than just the 0 element), and...

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Advance Math

Let R and S be nontrivial rings (i.e., containing more than justthe 0 element), and define the projection homomorphism pi_1: R X S--> R by pi_1(x,y)=x.

(a) Prove that pi_1 is a surjective homomorphism of rings.

(b) Prove that pi_1 is not injective

(c) Prove that (R X S)/R (not congruent) R.

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