## `Cat::RightModule` -- the category of right `R`-modules

#### Introduction

``Cat::RightModule`(R)` represents the caregory of right `R`-modules.

#### Generating the category

`Cat::RightModule(R)`

#### Parameters

`R` | - | A domain which must be from the category `Cat::Ring`.

#### Categories

`Cat::AbelianGroup`

#### Details

- 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 distibutive laws must hold:
  1. x (a b) = (x a) b,
  2. x (a + b) = x a + x b,
  3. (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.

#### Method _mult: right multiplication by a ring element

- `_mult(dom x, R r)`
- - Must return the right multiplication of `x` by the ring element `r`.

#### Changes

- no changes

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