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Category of right R-modules

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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:

  1. x (ab) = (xa) b,

  2. x (a + b) = xa + xb,

  3. (x + y) a = xa + ya.

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.


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Basic Methods

_mult(x, r)

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