. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
~
ross/maths/Quantum/Sect1.html#206
):
A rig is a set R enriched with two monoid structures, a commutative one written additively and the other written multiplicatively, such that the following equations hold:a0 = 0 = 0a
a(b + c) = ab + ac,(a + b)c = ac + ab
The natural numbers N provide an example of a rig.A ring is a rig for which the additive monoid is a group. The integers Z provide an example.
A rig is commutative when the multiplicative monoid is commutative.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .