Dense (mod 1) dilated semigroups of algebraic numbers

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6 Scopus citations


Given a real algebraic number field K we consider the following possible properties of a multiplicative subsemigroup S of K*: (1) Sα is dense modulo 1 for every α ∋ K. (2) Sα is dense modulo 1 for every α ≠ 0. A full characterization of those semigroups satisfying each of these properties is obtained. In particular, it follows that a semigroup possessing one of these properties has a subsemigroup, generated by two elements, with the same property. Given a finitely generated semigroup, one can effectively decide whether or not it satisfies either one of the aforementioned properties. A p-adic analogue of the main result is studied as well.

Original languageEnglish
Pages (from-to)246-256
Number of pages11
JournalJournal of Number Theory
Issue number3
StatePublished - 1 Jan 1987
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory


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