This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.


Category of left R -modules

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.




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.



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


expand all

Basic Methods

_mult(r, x)

Was this topic helpful?