prime field

prime field

English

Noun

prime field (plural prime fields)

1. (algebra, field theory) A field that contains no proper subfields.
   • 1968, J. F. Schuh, Mathematical Tools for Modern Physics, Philips Technical Library, page 91,

     Theorem 2. Each field contains a unique prime field.

   • 2004, H. Gopalkrishna Gadiyar, K. M. Sangeeta Maini, R. Padma, Cryptography, Connections, Cocycles and Crystals: A p-adic Exploration of the Discrete Logarithm Problem, Anne Canteaut, Kapaleeswaran Viswanathan (editors), Progress in Cryptology - INDOCRYPT 2004: 5th International Conference, Proceedings, Springer, LNCS 3348, page 305,

     Applying Hensel's lemma to the discrete logarithm problem over prime fields reveals the rich geometric and algebraic structure underlying the problem.

   • 2004, Leo Corry, Modern Algebra and the Rise of Mathematical Structures, Springer (Birkhäuser), 2nd Edition, page 194,

     Since every field contains a prime field, by studying prime fields, and the way properties are passed over to extensions, Steinitz would attain a full picture of the structure of all possible fields.

Translations

field that contains no subfields

Further reading

• Characteristic (algebra)#Case of fields on Wikipedia.Wikipedia
• Prime field on Encyclopedia of Mathematics