module
Let be a ring with identity. A left module over is a set with two binary operations, and , such that
-
1.
for all
-
2.
for all
-
3.
There exists an element such that for all
-
4.
For any , there exists an element such that
-
5.
for all and
-
6.
for all and
-
7.
for all and
A left module over is called unitary or unital if for all .
A (unitary or unital) right module is defined analogously, except that the function goes from to and the scalar multiplication operations act on the right. If is commutative, there is an equivalence of categories between the category of left –modules and the category of right –modules.
Title | module |
Canonical name | Module |
Date of creation | 2013-03-22 11:49:14 |
Last modified on | 2013-03-22 11:49:14 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 11 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 13-00 |
Classification | msc 16-00 |
Classification | msc 20-00 |
Classification | msc 44A20 |
Classification | msc 33E20 |
Classification | msc 30D15 |
Synonym | left module |
Synonym | right module |
Related topic | MaximalIdeal |
Related topic | VectorSpace |