and 
hold.Cat::SemiRng – the category of semi-rings without unit
Cat::SemiRng represents the category of semi-rings without unit.
Categories
Cat::AbelianMonoid, Cat::Monoid
Details:
A Cat::SemiRng is essentially a ring without unit (Cat::Rng), except that the operation + (_plus) is not required to be invertible. In other words, this is an abelian monoid according to the operation + and a non-Abelian semi-group according to the operation * (_mult) where in addition the two distributive laws and hold.