derivation
Let $R$ be a commutative ring. A derivation $d$ on an $R$algebra^{} $A$ into an $A$module $M$ is an $R$linear transformation $\mathrm{d}:A\to M$ satisfying the properties

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$\mathrm{d}(a\mathbf{x}+b\mathbf{y})=a\mathrm{d}\mathbf{x}+b\mathrm{d}\mathbf{y}$

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$\mathrm{d}(\mathbf{x}\cdot \mathbf{y})=\mathbf{x}\cdot \mathrm{d}\mathbf{y}+\mathrm{d}\mathbf{x}\cdot \mathbf{y}$
for all $a,b\in R$ and $\mathbf{x},\mathbf{y}\in A$.
Title  derivation 

Canonical name  Derivation 
Date of creation  20130322 12:02:41 
Last modified on  20130322 12:02:41 
Owner  djao (24) 
Last modified by  djao (24) 
Numerical id  10 
Author  djao (24) 
Entry type  Definition 
Classification  msc 17A36 
Classification  msc 16W25 
Classification  msc 13N15 