Difference between revisions of "Prime field"
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A [[field]] not containing proper subfields. Every field contains a unique prime field. A prime field of [[Characteristic of a field|characteristic]] 0 is [[Isomorphism|isomorphic]] to the field of [[rational number]]s. A prime field of [[Characteristic of a field|characteristic]] $p$ is [[Isomorphism|isomorphic]] to the field $\mathbb{Z}/p\mathbb{Z}$ of integers modulo $p$. | A [[field]] not containing proper subfields. Every field contains a unique prime field. A prime field of [[Characteristic of a field|characteristic]] 0 is [[Isomorphism|isomorphic]] to the field of [[rational number]]s. A prime field of [[Characteristic of a field|characteristic]] $p$ is [[Isomorphism|isomorphic]] to the field $\mathbb{Z}/p\mathbb{Z}$ of integers modulo $p$. | ||
Revision as of 19:26, 30 August 2013
2020 Mathematics Subject Classification: Primary: 12Exx [MSN][ZBL]
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=30272
Prime field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Prime_field&oldid=30272
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article