adic

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adic (not comparable)

1. (mathematics) Relating to adicity
   • 2015, Thierry Giordano, David Handelman, Radu B. Munteanu, “Nonsingular transformations and dimension spaces”, in arXiv‎:

     For any adic transformation ${\displaystyle T}$ defined on the path space ${\displaystyle X}$ of an ordered Bratteli diagram, endowed with a Markov measure ${\displaystyle \mu }$, we construct an explicit dimension space (which corresponds to a matrix values random walk on ${\displaystyle \mathbb {Z} }$) whose Poisson boundary can be identified as a ${\displaystyle \mathbb {Z} }$-space with the dynamical system ${\displaystyle (X,\mu ,T)}$.

2. (algebra, of topological ring) Carrying the ${\displaystyle I}$-adic topology for some ideal ${\displaystyle I}$ of the ring.

Some authors use the term pre-adic for the ring-theoretic sense given above, reserving the term adic for rings which are also complete with respect to this topology.

• ACID, Daic, acid, cadi, caid

• IPA^(key): (Central, Balearic)
• IPA^(key): (Valencia)

adic

1. only used in m'adic, first-person singular present indicative of adir-se