CONTROLLING DISTRIBUTION OF PRIME SEQUENCES IN DISCRETELY ORDERED PRINCIPAL IDEAL SUBRINGS OF Q[x]
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471311" target="_blank" >RIV/00216208:11320/23:10471311 - isvavai.cz</a>
Alternative codes found
RIV/61384399:31140/23:00058861
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=zlQWVLbaGg" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=zlQWVLbaGg</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/16358" target="_blank" >10.1090/proc/16358</a>
Alternative languages
Result language
angličtina
Original language name
CONTROLLING DISTRIBUTION OF PRIME SEQUENCES IN DISCRETELY ORDERED PRINCIPAL IDEAL SUBRINGS OF Q[x]
Original language description
We show how to construct discretely ordered principal ideal sub rings of Q[x] with various types of prime behaviour. Given any set V consisting of finite strictly increasing sequences (d(1), d(2), . . . , d(l)) of positive integers such that, for each prime integer p, the set {pZ, d(1)+pZ, . . . , d(l)+pZ} does not contain all the cosets modulo p, we can stipulate to have, for each (d(1), . . . , d(l)) is an element of D, a cofinal set of progressions (f, f + d(1), . . . , f + d(l)) of prime elements in our principal ideal domain R-tau. Moreover, we can simultaneously guarantee that each positive prime g is an element of R-tau N is either in a prescribed progression as above or there is no other prime h in R tau such that g - h is an element of Z. Finally, all the principal ideal domains we thus construct are non-Euclidean and isomorphic to subrings of the ring (Z) over cap of profinite integers.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
1088-6826
Volume of the periodical
151
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
3281-3290
UT code for WoS article
000988381200001
EID of the result in the Scopus database
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