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 $\mathrm{d}\colon A\to M$ satisfying the properties

•

$\mathrm{d}(a\mathbf{x}+b\mathbf{y})=a\,\mathrm{d}\mathbf{x}+b\,\mathrm{d}% \mathbf{y}$
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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	2013-03-22 12:02:41
Last modified on	2013-03-22 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