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  • 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. (en)
Title
  • A Note on Density and the Dirichlet Condition
  • A Note on Density and the Dirichlet Condition (en)
skos:prefLabel
  • A Note on Density and the Dirichlet Condition
  • A Note on Density and the Dirichlet Condition (en)
skos:notation
  • RIV/67985807:_____/12:00376593!RIV13-GA0-67985807
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  • P(GA201/07/0191), Z(AV0Z10300504)
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  • 3
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  • 120442
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  • RIV/67985807:_____/12:00376593
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  • 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 (en)
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  • SG - Singapurská republika
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  • [EF95798970BD]
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  • International Journal of Number Theory
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  • 8
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  • Porubský, Štefan
  • Marko, F.
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  • 000302020300017
http://linked.open...n/vavai/riv/zamer
issn
  • 1793-0421
number of pages
http://bibframe.org/vocab/doi
  • 10.1142/S1793042112500479
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