311: Left R-Module|T.B.P.

Topics

About: ring
About: module

For any multiplicatively-commutative ring, R, any additively-abelian group, M, together with scalar left multiplication by R,

R \times M \to M

, such that for any

r_{1}, r_{2} \in R

and

m_{1}, m_{2} \in M

, 1)

(r_{1} r_{2}) m_{1} = r_{1} (r_{2} m_{1})

; 2)

1 m_{1} = m_{1}

; 3)

(r_{1} + r_{2}) m_{1} = r_{1} m_{1} + r_{2} m_{1}

and

r_{1} (m_{1} + m_{2}) = r_{1} m_{1} + r_{1} m_{2}

It is a generalization of vector space, allowing a ring in scalar multiplication than a field.

The Bias Planet
Definitions and Propositions
School Mathematics from Higher Viewpoints
To Disentangle Confusing Terms or Discourses
Information Tables
Exploiting LibreOffice or OpenOffice
Exposing the Java Programming Language
Exposing C++
Exposing Python
Exposing C#
Exposing Gradle
Exposing Git
UNO Dispatch Commands