For any x,y E R (i.e. Ring R) the following equalities hold.
Prove either a or b. State any properties used in your proof.
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For any x, y R (i.e. ring R), the following equalities hold:
a) 0 x = 0
b) a(-b) = (-a)b = -(ab)
Prove either (a) or (b). State any properties used in your proof.
We will prove the above equalities based on the axioms of a ring.
a) Any ring is a commutative group with respect to "addition" law, that is for any a R, there exists (-a) R so that:
Ring identities are proven. The solution is detailed and well presented.