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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 5, Pages 1080–1088 (Mi izv2192)  

This article is cited in 1 scientific paper (total in 1 paper)

Adèles and integral representations

Yu. A. Drozd


Abstract: We apply the technique of adèles to study integral representations belonging to the same genus. We study the stable structure of genera and prove that if $L$ is a representation of a semisimple $Z$-ring such that each direct summand occurs at least twice in the decomposition of $L$ over the field of rational numbers, and if $M$ and $N$ are representations from the genus of $L$, then $M\oplus L^n\simeq N\oplus L^n$ implies that $M\simeq N$. For representations of a semisimple $Z$-ring $\Lambda$ we give a bound for the number of representations in a genus; the bound depends only on the rational algebra $\widetilde\Lambda=\Lambda\otimes Q$ and on the exponent of the group $\Lambda'/\lambda$ , where $\Lambda'$ is a maximal overring of $\Lambda$.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:5, 1019–1026

Bibliographic databases:

UDC: 519.49
MSC: 20C10, 11S23, 11R56
Received: 24.06.1968

Citation: Yu. A. Drozd, “Adèles and integral representations”, Izv. Akad. Nauk SSSR Ser. Mat., 33:5 (1969), 1080–1088; Math. USSR-Izv., 3:5 (1969), 1019–1026

Citation in format AMSBIB
\Bibitem{Dro69}
\by Yu.~A.~Drozd
\paper Ad\`eles and integral representations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 5
\pages 1080--1088
\mathnet{http://mi.mathnet.ru/izv2192}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=255595}
\zmath{https://zbmath.org/?q=an:0208.04502|0212.38006}
\transl
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 5
\pages 1019--1026
\crossref{https://doi.org/10.1070/IM1969v003n05ABEH000822}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Robert M Guralnick, “The genus of a module II. Roiter's theorem, power cancellation and extension of scalars”, Journal of Number Theory, 26:2 (1987), 149  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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