-adic

See also: adic

English

Etymology

Back-formation from monadic, etc., from Ancient Greek -άς (-ás) (genitive -άδος (-ádos)) + -ικός (-ikós) (English -ad + -ic). Compare related adicity and Latinate -ary.

The algebraic sense is by analogy with p-adic, since $\mathbb {Z} _{(p)}$ equipped with the $(p)$-adic topology passes to the ring of p-adic numbers under the operation of completion.

Pronunciation

• Audio (US):

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Suffix

-adic

1. (mathematics, computing) Having a specified adicity.
2. (algebra, of a topology on a module $M$ over a ring $R$, combined with a symbol (here $I$ but also often $p$, $m$, or $a$) representing an ideal of $R$) Such that the sets $x+I^{n}M$ (where $x\in M$, $n$ a non-negative integer) form a basis for the topology.

Usage notes

Combined with prefixes derived (usually) from Greek names for numbers to make adjectives meaning "having a certain number of arguments" (said of functions, relations, etc, in mathematics and functions, operators, etc, in computing).

Since there is a unique $I$-adic topology for any given $I$, one often speaks of the $I$-adic topology on $M$.

Synonyms

• (adicity): -ary

Derived terms

English terms suffixed with -adic

Related terms

terms related to -adic

• decadic
• duadic
• dyadic
• enneadic
• heptadic
• hexadic
• monadic
• n-adic
• niladic
• nonadic
• octadic
• p-adic
• pentadic
• polyadic
• tetradic
• triadic
• variadic

Translations

having a number of arguments

• Finnish: -adinen
• French: -adique
• German: -adisch
• Hungarian: -adikus
• Italian: -adico
• Polish: not used in Polish
• Romanian: -adic

See also

• Appendix:English arities and adicities

Anagrams

• ACID, Daic, acid, cadi, caid