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Cat::Rng

Category of rings without unit

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Description

Cat::Rng represents the category of rings without unit.

A Cat::Rng is a ring without a unit, i.e. an Abelian group according to the operation + (_plus) and a non-Abelian semi-group according to the operation * (_mult) where in addition the two distributive laws a (b + c) = ab + ac and (a + b) c = ac + bc hold.

Use the axiom Ax::noZeroDivisors to state that there are no zero divisors according to *, i.e. that the product of non-zero elements never is zero.