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Zap. Nauchn. Sem. POMI, 2007, Volume 349, Pages 211–241 (Mi znsl59)  

This article is cited in 3 scientific papers (total in 3 papers)

Generalized subrings of arithmetic rings

A. L. Smirnov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: The generalized subrings of $\mathbb{F}_q$ are classified, generalized subrings of $\mathbb{Z}/p^2$ are investigated and their complete classification is obtained when $p=2$. Examples of $\mathbb{F}_\infty$-similar generalized fields, a computation of $\mathbb{F}_\infty^{\otimes n}$, a description of cofinite subrings of $\mathbb{Z}_p$ and examples of subrimgs of $\mathbb{Z}_\infty$ are given. A conjecture on cofinite subrings of $\mathbb{Z}$ is proposed and arguments in its favour are considered.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:3, 3052–3068

UDC: 512.5
Received: 30.10.2007

Citation: A. L. Smirnov, “Generalized subrings of arithmetic rings”, Problems in the theory of representations of algebras and groups. Part 16, Zap. Nauchn. Sem. POMI, 349, POMI, St. Petersburg, 2007, 211–241; J. Math. Sci. (N. Y.), 151:3 (2008), 3052–3068

Citation in format AMSBIB
\Bibitem{Smi07}
\by A.~L.~Smirnov
\paper Generalized subrings of arithmetic rings
\inbook Problems in the theory of representations of algebras and groups. Part~16
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 349
\pages 211--241
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl59}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 151
\issue 3
\pages 3052--3068
\crossref{https://doi.org/10.1007/s10958-008-9014-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49249106104}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J. Math. Sci. (N. Y.), 192:2 (2013), 234–242  mathnet  crossref  mathscinet
    2. S. A. Evdokimov, “Proof of the congruence conjecture for generalized rings”, J. Math. Sci. (N. Y.), 222:4 (2017), 426–428  mathnet  crossref  mathscinet
    3. A. L. Smirnov, “Neklassicheskie biratsionalnye modeli $\operatorname{Spec}\mathbb Q$”, Voprosy teorii predstavlenii algebr i grupp. 31, Zap. nauchn. sem. POMI, 455, POMI, SPb., 2017, 181–196  mathnet
  • Записки научных семинаров ПОМИ
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