Category of right R-modules
This functionality does not run in MATLAB.
Cat::RightModule(R) represents the caregory of right R-modules.
A Cat::RightModule is an Abelian group together with a ring R and a right multiplication * (_mult).
The right multiplication is an operation taking an element of ring R and a module element and returning a module element.
Given ring elements a, b and module elements x, y the following 3 distributive laws must hold:
x (a b) = (x a) b,
x (a + b) = x a + x b,
(x + y) a = x a + y a.
Beware: The operation of a non-Abelian semi-group is also written as * (_mult). The method "_mult" must handle the situation if a right module is also a non-Abelian semi-group. In such a case it must both implement the group operation and the right multiplication by elements of the ring.
A domain which must be from the category Cat::Ring.