On the compositum of orthogonal cyclic fields of the same odd prime degree
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00118788" target="_blank" >RIV/00216224:14310/21:00118788 - isvavai.cz</a>
Result on the web
<a href="https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/abs/on-the-compositum-of-orthogonal-cyclic-fields-of-the-same-odd-prime-degree/1165F270D43F1AF619B6656FD07BEA54" target="_blank" >https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/abs/on-the-compositum-of-orthogonal-cyclic-fields-of-the-same-odd-prime-degree/1165F270D43F1AF619B6656FD07BEA54</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4153/S0008414X20000589" target="_blank" >10.4153/S0008414X20000589</a>
Alternative languages
Result language
angličtina
Original language name
On the compositum of orthogonal cyclic fields of the same odd prime degree
Original language description
The aim of this paper is to study circular units in the compositum K of t cyclic extensions of Q (t ≥ 2) of the same odd prime degree ℓ. If these fields are pairwise arithmetically orthogonal and the number s of primes ramifying in K/Q is larger than t, then a nontrivial root ε of the top generator η of the group of circular units of K is constructed. This explicit unit ε is used to define an enlarged group of circular units of K, to show that ℓ^{(s−t)ℓ^{t−1}} divides the class number of K, and to prove an annihilation statement for the ideal class group of K.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-11473S" target="_blank" >GA18-11473S: The ideal class groups of abelian extensions of some number fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Canadian Journal of Mathematics-Journal canadien de mathématiques
ISSN
0008-414X
e-ISSN
1496-4279
Volume of the periodical
73
Issue of the periodical within the volume
6
Country of publishing house
GB - UNITED KINGDOM
Number of pages
25
Pages from-to
1506-1530
UT code for WoS article
000729499500004
EID of the result in the Scopus database
2-s2.0-85122403018