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Let $R$ be a commutative ring. A derivation $d$ on an $R$ -algebra $A$ into an $A$ -module $M$ is an $R$ -linear transformation $\d\colon A \to M$ satisfying the properties
- $\d(a\x+b\y) = a\,\d\x + b\,\d\y$
- $\d(\x\cdot \y) = \x \cdot \d\y + \d\x \cdot \y$
for all $a,b \in R$ and $\x,\y \in A$ .
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"derivation" is owned by djao. [ full author list (2) ]
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Cross-references: properties, transformation, commutative ring
There are 68 references to this entry.
This is version 6 of derivation, born on 2001-12-12, modified 2005-09-15.
Object id is 1089, canonical name is Derivation.
Accessed 10154 times total.
Classification:
| AMS MSC: | 13N15 (Commutative rings and algebras :: Differential algebra :: Derivations) | | | 16W25 (Associative rings and algebras :: Rings and algebras with additional structure :: Derivations, actions of Lie algebras) | | | 17A36 (Nonassociative rings and algebras :: General nonassociative rings :: Automorphisms, derivations, other operators) |
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Pending Errata and Addenda
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