https://subwiki.org/w/index.php?action=history&feed=atom&title=Characteristic_%28mathematics%29 2026-05-04T15:58:08Z Revision history for this page on the wiki MediaWiki 1.41.2 https://subwiki.org/w/index.php?title=Characteristic_(mathematics)&diff=16&oldid=prev 2008-05-13T02:02:05Z

<p>New page: The term &#039;&#039;characteristic&#039;&#039; in mathematics typically stands for: * Something specific, unique, intrinsic or invariant to the situation * Something that completely describes the given situ...</p> <p><b>New page</b></p><div>The term &#039;&#039;characteristic&#039;&#039; in mathematics typically stands for:<br /> <br /> * Something specific, unique, intrinsic or invariant to the situation<br /> * Something that completely describes the given situation<br /> <br /> Related terms are &#039;&#039;invariant&#039;&#039;.<br /> <br /> ===In commutative algebra/field theory===<br /> <br /> [[Commalg:Characteristic of a ring|Characteristic of a ring]]: The smallest positive integer &lt;math&gt;n&lt;/math&gt; such that &lt;math&gt;n.1 = 0&lt;/math&gt;. If no such positive integer exists, then the characteristic is said to be zero. A field either has characteristic zero or has characteristic equal to a prime number.<br /> <br /> ===In group theory===<br /> <br /> [[Groupprops:Characteristic subgroup|Characteristic subgroup]]: A subgroup that is invariant (or, gets mapped to itself) under any automorphism of the group.<br /> <br /> ===In algebraic topology/differential geometry===<br /> <br /> [[Diffgeom:Characteristic class|Characteristic class]]: A natural transformation from the vector bundle functor to the cohomology functor on a manifold; in other words, it assigns to every vector bundle over a manifold, a cohomology class, such that a certain naturality diagram commutes.<br /> <br /> ===In measure theory/analysis===<br /> <br /> [[Find link::Characteristic function]] of a set, also called its indicator function, is a function that takes value 1 on the set and 0 outside it.<br /> <br /> ===In probability/statistics===<br /> <br /> ===Others===<br /> <br /> [[Find link::Characteristic series]]</div>

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