Difference between revisions of "Differential ring"
From Encyclopedia of Mathematics
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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 $A$. | 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
2020 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
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