Differential-algebra(2)
From Encyclopedia of Mathematics
An algebra over a field (ring) K which is a differential ring and such that, moreover, any derivation \partial commutes with multiplications by elements of K, i.e. \partial(\alpha x) = \alpha \partial(x), where \alpha \in K, x \in A.
Comments
Cf. also Derivation in a ring.
A differential graded algebra (or DGA) over a ring K is a graded algebra A equipped with a graded K-module homomorphism \partial : A \rightarrow A of degree -1 such that \partial^2 = 0 and such that \partial is a derivation in the graded sense, i.e. such that \partial(uv) = \partial(u) v + (-1)^{\deg u} u \partial(v). They are of importance in (co)homology theory.
References
[a1] | S. MacLane, "Homology" , Springer (1963) |
How to Cite This Entry:
Differential-algebra(2). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Differential-algebra(2)&oldid=39583
Differential-algebra(2). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Differential-algebra(2)&oldid=39583
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article