Difference between revisions of "Prime field"
From Encyclopedia of Mathematics
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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 $p$, often denoted $\mathbb{F}_p$ or $\mathrm{GF}(p)$. |
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| + | ====References==== | ||
| + | <table> | ||
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> Paul J. McCarthy, "Algebraic Extensions of Fields", Courier Dover Publications (2014) {{ISBN|048678147X}} </TD></TR> | ||
| + | </table> | ||
Latest revision as of 19:39, 27 October 2023
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 $p$, often denoted $\mathbb{F}_p$ or $\mathrm{GF}(p)$.
References
| [1] | Paul J. McCarthy, "Algebraic Extensions of Fields", Courier Dover Publications (2014) ISBN 048678147X |
How to Cite This Entry:
Prime field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Prime_field&oldid=31046
Prime field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Prime_field&oldid=31046
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article