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Cat::LeftModule

Category of left R -modules

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

Cat::LeftModule(R)

Description

Cat::LeftModule(R) represents the category of left R-modules.

A Cat::LeftModule(R) is an Abelian group together with a rng R (a ring without unit) and a left multiplication * (_mult).

The left multiplication is an operation taking an element of rng 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. (ab) x = a (bx),

  2. (a + b) x = ax + bx,

  3. a (x + y) = ax + ay.

Beware: The operation of a non-Abelian semi-group is also written as * (_mult). The method "_mult" must 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.

Parameters

R

A domain which must be from the category Cat::Rng.

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