RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

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

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 $\Lambda$.

Full text: PDF file (1098 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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

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} `

• http://mi.mathnet.ru/eng/izv2192
• http://mi.mathnet.ru/eng/izv/v33/i5/p1080

 SHARE:

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
•  Number of views: This page: 244 Full text: 82 References: 51 First page: 1