Differential Algebra
A differential algebra over a field K is a K-algebra A wherein the derivation(s) commutes with the field. That is, for all and one has
In index-free notation, if is the ring morphism defining scalar multiplication on the algebra, one has
As above, the derivation must obey the Leibniz rule over the algebra multiplication, and must be linear over addition. Thus, for all and one has
and
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