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    Ring Identities

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    For any x,y E 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.

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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:

    Solution Summary

    Ring identities are proven. The solution is detailed and well presented.