A note on density and the dirichlet condition

František Marko, Štefan Porubský

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Motivated by topological approaches to Euclid and Dirichlet's theorems on infinitude of primes, we introduce and study S-coprime topologies on a commutative ring R with an identity and without zero divisors. For infinite semiprimitive commutative domain R of finite character (i.e. every nonzero element of R is contained in at most finitely many maximal ideals of R), we characterize its subsets A for which the Dirichlet condition, requiring the existence of infinitely many pairwise nonassociated elements from A in every open set in the invertible topology, is satisfied.

Original languageEnglish (US)
Pages (from-to)823-830
Number of pages8
JournalInternational Journal of Number Theory
Volume8
Issue number3
DOIs
StatePublished - May 1 2012

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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