Category of left R -modules
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Cat::LeftModule(R) represents the category
Cat::LeftModule(R) is an Abelian group
together with a rng
R (a ring without unit) and
a left multiplication
The left 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 distibutive laws must hold:
(a b) x = a (b x),
(a + b) x = a x + b x,
a (x + y) = a x + a y.
Beware: The operation of a non-Abelian semi-group is also written
_mult). The method
handle the situation if a left module is also a non-Abelian semi-group.
In such a case it must both implement the group operation and the
left multiplication by elements of the rng.
A domain which must be from the category
_mult— Left multiplication by a rng element