nLab
differential algebra

Idea

A differential algebra is an associative algebra $A$ equipped with a derivation $d \colon A \to A$, typically required to satisfy $d \circ d = 0$.

If $A$ is a field one accordingly speaks of a differential field.

If $A$ is a graded algebra and $d$ is of degree 1 one speaks of a differential graded algebra.

Etc.

Related concepts

• differential ideal

• differential graded algebra

• differential graded-commutative algebra

• differential algebroid

References

• differential Galois theory

algebraic structure	oidification
truth value	transitive relation
magma	magmoid
unital magma	unital magmoid
quasigroup	quasigroupoid
loop	loopoid
semigroup	semicategory
monoid	category
associative quasigroup	associative quasigroupoid
group	groupoid
flexible magma	flexible magmoid
alternative magma	alternative magmoid
absorption monoid	absorption category
(left,right) cancellative monoid	(left,right) cancellative category
rig	CMon-enriched category
nonunital ring	Ab-enriched semicategory
nonassociative ring	Ab-enriched unital magmoid
ring	ringoid
differential ring?	differential ringoid?
nonassociative algebra	linear magmoid
nonassociative unital algebra	unital linear magmoid
nonunital algebra	linear semicategory
associative unital algebra	linear category
C-star algebra	C-star category
differential algebra	differential algebroid
flexible algebra	flexible linear magmoid
alternative algebra	alternative linear magmoid
Lie algebra	Lie algebroid
strict monoidal category	strict 2-category
strict 2-group	strict 2-groupoid
monoidal poset?	2-poset
monoidal groupoid?	(2,1)-category
monoidal category	2-category/bicategory
2-group	2-groupoid/bigroupoid