Prime field

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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 $\mathrm{GF}(p)$.


[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:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article