a,b,c in R, a not 0, ab=ac implies b=c

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a,b, in R, ab=0 implies a=0 or b=0

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a in R implies, a not 0, a^2 = a implies a=0 or a=1.

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There exists R, there exists a,b, in R s.t.
ab=0 and (a=0 or b=0)

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There exists R, there exists a in R s.t. a not 0, a^2=a and
(a=0 or a=1)

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There exists R, there exists a,b,c in R s.t. a not 0, ab=ac and b=c.

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