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Zap. Nauchn. Sem. LOMI, 1982, Volume 116, Pages 5–13 (Mi znsl1746)  

Net determinant over a Bezoutian local ring

Z. I. Borevich, N. A. Vavilov


Abstract: Let $\sigma$ be any $D$-net of ideals of order $n$ over a commutative local Bezoutian ring $R$ and denote by $G(\sigma)$ the corresponding net subgroup in the general linear group of degree $n$ over $R$ (RZhMat, 1977, 2A280). We give an explicit computation of the factor group $G(\sigma)/E(\sigma)$, where $E(\sigma)$ is the subgroup generated by all elementary transvections in $G(\sigma)$.

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English version:
Journal of Soviet Mathematics, 1984, 26:3, 1839–1844

Bibliographic databases:

UDC: 519.46

Citation: Z. I. Borevich, N. A. Vavilov, “Net determinant over a Bezoutian local ring”, Integral lattices and finite linear groups, Zap. Nauchn. Sem. LOMI, 116, "Nauka", Leningrad. Otdel., Leningrad, 1982, 5–13; J. Soviet Math., 26:3 (1984), 1839–1844

Citation in format AMSBIB
\Bibitem{BorVav82}
\by Z.~I.~Borevich, N.~A.~Vavilov
\paper Net determinant over a Bezoutian local ring
\inbook Integral lattices and finite linear groups
\serial Zap. Nauchn. Sem. LOMI
\yr 1982
\vol 116
\pages 5--13
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1746}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=687835}
\zmath{https://zbmath.org/?q=an:0541.20034|0517.20025}
\transl
\jour J. Soviet Math.
\yr 1984
\vol 26
\issue 3
\pages 1839--1844
\crossref{https://doi.org/10.1007/BF01670567}


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