Standard Lemma guide

p-adic

adj · 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

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

No pronunciation record was provided for this word.

1

adj

Meaning 1

Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: mathematics, number-theory, sciences

Examples

  • 1997, Fernando Q. Gouvêa, p-adic Numbers: An Introduction, Springer, 2nd Edition, page 60, Definition 3.3.3 The ring of p'''-adic integers is the valuation ring Z p=x∈ Q p:|x|p<1.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

From p + -adic. The letter p follows common number theory usage in representing an arbitrary prime number; the suffix -adic signals that properties of the number p (generally, those due to its being prime, and specifically those of a specified p) are fundamental to the theory and determine the properties of the resulting construction.

Across languages

Translations

9 source translations are retained for this English entry.

  • Catalan: p-àdic — Translations
  • Finnish: p-adinen — Translations
  • French: p-adique — Translations
  • German: p-adisch — Translations
  • Italian: p-adico — Translations
  • Polish: p-adyczny — Translations
  • Portuguese: p-ádico — Translations
  • Romanian: p-adic — Translations
  • Spanish: p-ádico — Translations