An algebra over a field (ring) which is a differential ring and such that, moreover, any derivation commutes with multiplications by elements of , i.e. , where , .
Cf. also Derivation in a ring. A differential graded algebra (or DGA) over a ring is a graded algebra equipped with a graded -module homomorphism of degree such that and such that is a derivation in the graded sense, i.e. such that . They are of importance in (co)homology theory.
|[a1]||S. MacLane, "Homology" , Springer (1963)|
Differential-algebra(2). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Differential-algebra(2)&oldid=15881