#matrices with elements from a ring R with matrix addition and scalar multiplication defined by component-wise left multiplication

[maths-terms-identifier]

Module

Abstract Algebra

Let R be a ring, then a left R-module, M is an Abelian group (M,+) along with an operation ·:R×M->M such that for all r,s∈R and x,y∈M we have

r·(x+y)=r·x+r·y,

(r+s)·x=r·x+s·x

(r·s)·x=r·(s·x)

1·x=x

+ is called addition and · is called scalar multiplication

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