Phrase guide

prime field

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A field that contains no proper subfields.

Definition source: English Wiktionary via Wiktextract

Qualifier: field theory

Topics: algebra, mathematics, sciences

Examples

  • 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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

1 source translations are retained for this English entry.

  • Polish: ciało pierwsze — field that contains no subfields