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Statements

Subject Item
n2:RIV%2F67985807%3A_____%2F12%3A00376593%21RIV13-GA0-67985807
rdf:type
skos:Concept n10:Vysledek
dcterms:description
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. 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.
dcterms:title
A Note on Density and the Dirichlet Condition A Note on Density and the Dirichlet Condition
skos:prefLabel
A Note on Density and the Dirichlet Condition A Note on Density and the Dirichlet Condition
skos:notation
RIV/67985807:_____/12:00376593!RIV13-GA0-67985807
n10:predkladatel
n11:ico%3A67985807
n3:aktivita
n6:P n6:Z
n3:aktivity
P(GA201/07/0191), Z(AV0Z10300504)
n3:cisloPeriodika
3
n3:dodaniDat
n5:2013
n3:domaciTvurceVysledku
n4:9984038
n3:druhVysledku
n20:J
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n19:predkladatel
n3:idSjednocenehoVysledku
120442
n3:idVysledku
RIV/67985807:_____/12:00376593
n3:jazykVysledku
n7:eng
n3:klicovaSlova
Coset topology; topological semigroup; topological density; Dirichlet theorem on primes; arithmetical progression; maximal ideal; ring of finite character; h-local domain; residually finite ring; pseudoprime
n3:klicoveSlovo
n8:Coset%20topology n8:residually%20finite%20ring n8:pseudoprime n8:topological%20density n8:topological%20semigroup n8:h-local%20domain n8:maximal%20ideal n8:ring%20of%20finite%20character n8:arithmetical%20progression n8:Dirichlet%20theorem%20on%20primes
n3:kodStatuVydavatele
SG - Singapurská republika
n3:kontrolniKodProRIV
[EF95798970BD]
n3:nazevZdroje
International Journal of Number Theory
n3:obor
n17:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n16:GA201%2F07%2F0191
n3:rokUplatneniVysledku
n5:2012
n3:svazekPeriodika
8
n3:tvurceVysledku
Porubský, Štefan Marko, F.
n3:wos
000302020300017
n3:zamer
n12:AV0Z10300504
s:issn
1793-0421
s:numberOfPages
8
n15:doi
10.1142/S1793042112500479