Topological aspects of infinitude of primes in arithmetic progressions
Colloquium Mathematicum, Tome 140 (2015) no. 2, pp. 221-237
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We investigate properties of coset topologies on commutative domains with an identity, in particular, the $\mathcal {S}$-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 $\mathcal {S}$-coprime topologies on $\mathbb {Z}$. Finally, we give a new proof for the infinitude of prime ideals in number fields.
Keywords:
investigate properties coset topologies commutative domains identity particular mathcal coprime topologies defined nbsp marko nbsp porubsk nbsp akin topology defined furstenberg his proof infinitude rational primes extend results about infinitude prime maximal ideals related dirichlet theorem infinitude primes knopfmacher porubsk correct results paper determine cluster points set primes sets primes appearing arithmetic progressions mathcal coprime topologies mathbb finally proof infinitude prime ideals number fields
Affiliations des auteurs :
František Marko 1 ; Štefan Porubský 2
@article{10_4064_cm140_2_5,
author = {Franti\v{s}ek Marko and \v{S}tefan Porubsk\'y},
title = {Topological aspects of infinitude of primes in arithmetic progressions},
journal = {Colloquium Mathematicum},
pages = {221--237},
publisher = {mathdoc},
volume = {140},
number = {2},
year = {2015},
doi = {10.4064/cm140-2-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm140-2-5/}
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František Marko; Štefan Porubský. Topological aspects of infinitude of primes in arithmetic progressions. Colloquium Mathematicum, Tome 140 (2015) no. 2, pp. 221-237. doi: 10.4064/cm140-2-5
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