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Difference between revisions of "Differential ring"

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A ring with one or more distinguished derivations (cf. [[Derivation in a ring|Derivation in a ring]]). If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d032/d032280/d0322801.png" /> for all these derivations, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d032/d032280/d0322802.png" /> is said to be a constant.
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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 $A$.
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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.

Latest revision as of 19:54, 31 October 2016

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=12908
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article