# Prime field

From Encyclopedia of Mathematics

2010 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=34456

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