Category of rings without unit
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Cat::Rng represents the category of rings
Cat::Rng is a ring without a unit, i.e.
an Abelian group according to the operation
and a non-Abelian semi-group according to the operation
where in addition the two distributive laws a (b + c)
= a b + a c and (a + b) c = a c + b c hold.
Use the axiom
state that there are no zero divisors according to
i.e. that the product of non-zero elements never is zero.