Topological aspects of infinitude of primes in arithmetic progressions

František Marko, štefan Porubský

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate properties of coset topologies on commutative domains with an identity, in particular, the S-coprime topologies de ned by Marko and Poru-bsky (2012) and akin to the topology de ned by Furstenberg (1955) in his proof of the in nitude of rational primes. We extend results about the in nitude of prime or maximal ideals related to the Dirichlet theorem on the in nitude of primes from Knopfmacher and Porubsky (1997), and correct some results from that paper. Then we determine cluster points for the set of primes and sets of primes appearing in arithmetic progressions in S-coprime topologies on ℤ. Finally, we give a new proof for the infinitude of prime ideals in number fields.

Original languageEnglish (US)
Pages (from-to)221-237
Number of pages17
JournalColloquium Mathematicum
Volume140
Issue number2
DOIs
StatePublished - Jul 15 2015

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Arithmetic sequence
Topology
Coprime
Prime Ideal
Dirichlet's theorem
Maximal Ideal
Coset
Number field

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Topological aspects of infinitude of primes in arithmetic progressions. / Marko, František; Porubský, štefan.

In: Colloquium Mathematicum, Vol. 140, No. 2, 15.07.2015, p. 221-237.

Research output: Contribution to journalArticle

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