-adic

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 ${\displaystyle \mathbb {Z} _{(p)}}$ equipped with the ${\displaystyle (p)}$-adic topology passes to the ring of p-adic numbers under the operation of completion.

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-adic

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

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 ${\displaystyle I}$-adic topology for any given ${\displaystyle I}$, one often speaks of the ${\displaystyle I}$-adic topology on ${\displaystyle M}$.

• (adicity): -ary

• Appendix:English arities and adicities

• ACID, Daic, acid, cadi, caid