-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 $ℤ_{(p)}$ equipped with the $(p)$ -adic topology passes to the ring of p-adic numbers under the operation of completion.

Pronunciation

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Suffix

-adic

(mathematics, computing) Having a specified adicity.
(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 $M$ .