Category of right R-modules
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Cat::RightModule(R) represents the caregory
Cat::RightModule is an Abelian group together
with a ring
R and a right multiplication
The right multiplication is an operation taking an element of
R and a module element and returning a module
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
_mult). The method
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
_mult— Right multiplication by a ring element