Topological Aspects of Infinitude of Primes in Arithmetic Progressions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00446412" target="_blank" >RIV/67985807:_____/15:00446412 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4064/cm140-2-5" target="_blank" >http://dx.doi.org/10.4064/cm140-2-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/cm140-2-5" target="_blank" >10.4064/cm140-2-5</a>

Result language
angličtina
Original language name
Topological Aspects of Infinitude of Primes in Arithmetic Progressions
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP201%2F12%2F2351" target="_blank" >GAP201/12/2351: Distribution and metric properties of number sequences and their applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)