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Difference between revisions of "Prime field"

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A [[Field|field]] not containing proper subfields. Every field contains a unique prime field. A prime field of characteristic 0 is isomorphic to the field of rational numbers. A prime field of characteristic <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074500/p0745001.png" /> is isomorphic to the field <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074500/p0745002.png" /> of integers modulo <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074500/p0745003.png" />.
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A [[field]] not containing proper subfields. Every field contains a unique prime field. A prime field of characteristic 0 is isomorphic to the field of rational numbers. A prime field of characteristic $p$ is isomorphic to the field $\mathbb{Z}/p\mathbb{Z}$ of integers modulo $p$.

Revision as of 19:20, 30 August 2013

A field not containing proper subfields. Every field contains a unique prime field. A prime field of characteristic 0 is isomorphic to the field of rational numbers. A prime field of characteristic $p$ is isomorphic to the field $\mathbb{Z}/p\mathbb{Z}$ of integers modulo $p$.

How to Cite This Entry:
Prime field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Prime_field&oldid=17196
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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