prime field
English
Noun
prime field (plural prime fields)
- (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, 2nd edition, Springer (Birkhäuser), 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.
- 1968, J. F. Schuh, Mathematical Tools for Modern Physics, Philips Technical Library, page 91,
Translations
field that contains no subfields
Further reading
Characteristic (algebra) on Wikipedia.Wikipedia - Prime field on Encyclopedia of Mathematics
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