# Differential ring

From Encyclopedia of Mathematics

Revision as of 19:54, 31 October 2016 by Richard Pinch (talk | contribs) (transfer definition from differential field)

2010 Mathematics Subject Classification: *Primary:* 16W25 [MSN][ZBL]

A ring $A$ with one or more distinguished derivations (cf. Derivation in a ring). An element $a \in A$ such that $d(a) = 0$ for all these derivations $d$ is said to be a *constant*. The constants form a subring of $A$.

A **differential field** is a differential ring that is a field. The set of constants of a differential field is a subfield, the so-called field of constants.

**How to Cite This Entry:**

Differential ring.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Differential_ring&oldid=39574

This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article