prime field
Hello, you have come here looking for the meaning of the word prime field. In DICTIOUS you will not only get to know all the dictionary meanings for the word prime field, but we will also tell you about its etymology, its characteristics and you will know how to say prime field in singular and plural. Everything you need to know about the word prime field you have here. The definition of the word prime field will help you to be more precise and correct when speaking or writing your texts. Knowing the definition ofprime field, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.
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
