-adic

English

Etymology

Template:Back-formation, etc., from Template:Der (genitive Template:M) + Template:M (English Template:M + Template:M). Compare related Template:M and Latinate Template:M.

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

Pronunciation

• Template:Audio

Suffix

1. Template:Lb Having a specified adicity.
2. Template:Lb 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

• Template:Sense Template:L

Translations

• Finnish: Template:T
• French: Template:T
• German: Template:T
• Hungarian: Template:T
• Italian: Template:T
• Polish: Template:Not used
• Romanian: Template:T

See also

• Appendix:English arities and adicities

Anagrams

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