CNS rings. (English) Zbl 0558.10006

Topics in classical number theory, Colloq. Budapest 1981, Vol. II, Colloq. Math. Soc. János Bolyai 34, 961-971 (1984).
[For the entire collection see Zbl 0541.00002.]
A ring R is called a CNS ring if there exist an element \(\alpha\in R\) and a set \(N_ 0=\{0,1,...,n\}\) such that every \(\gamma\in R\) can be uniquely represened in the form \(\gamma =a_ 0+a_ 1\alpha +...+a_ ma^ m\) \((a_ i\in N_ 0)\). The paper presents a collection of results about CNS rings. In case R is the ring of integers of a quadratic number field the sets \(\{\alpha,N_ 0\}\) are completely determined, but some results for number fields of degree greater than two and for Abelian groups are also mentioned. There are some unsolved problems in the paper, too.
Reviewer: P.Kiss


11A63 Radix representation; digital problems
11R04 Algebraic numbers; rings of algebraic integers


Zbl 0541.00002