A Note on Density and the Dirichlet Condition
Result 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 domainR 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 elementsfrom A in every open set in the invertible topology, is satisfied.
Keywords
Coset topologytopological semigrouptopological densityDirichlet theorem on primesarithmetical progressionmaximal idealring of finite characterh-local domainresidually finite ringpseudoprime
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
A Note on Density and the Dirichlet Condition
Original language 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 domainR 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 elementsfrom A in every open set in the invertible topology, is satisfied.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
GA201/07/0191: Algebraic, analytic and combinatorial number theory
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Number Theory
ISSN
1793-0421
e-ISSN
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Volume of the periodical
8
Issue of the periodical within the volume
3
Country of publishing house
SG - SINGAPORE
Number of pages
8
Pages from-to
823-830
UT code for WoS article
000302020300017
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2012