Topological aspects of infinitude of primes in arithmetic progressions

• Autorzy: František Marko , Štefan Porubský
• Języki publikacji: EN

Abstrakty

EN

We investigate properties of coset topologies on commutative domains with an identity, in particular, the 𝓢-coprime topologies defined by Marko and Porubský (2012) and akin to the topology defined by Furstenberg (1955) in his proof of the infinitude of rational primes. We extend results about the infinitude of prime or maximal ideals related to the Dirichlet theorem on the infinitude of primes from Knopfmacher and Porubský (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.

Kategorie tematyczne

• 22A99: None of the above, but in this section
• 11N25: Distribution of integers with specified multiplicative constraints
• 11A25: Arithmetic functions; related numbers; inversion formulas
• 11N80: Generalized primes and integers
• 22A15: Structure of topological semigroups
• 11B05: Density, gaps, topology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 140
• Numer: 2
• Strony: 221-237

Daty

wydano

2015

Twórcy

autor

František Marko

• Pennsylvania State University, 76 University Drive, Hazleton, PA 18202, U.S.A.

autor

Štefan Porubský

• Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/cm140-2-5