Abstract
Let σ be any D-net of ideals of order n over a commutative local Bezoutian ring R and denote by G(σ) 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(σ)/E(σ), where E(σ) is the subgroup generated by all elementary transvections in G(σ).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
Z. I. Borevich, “Parabolic subgroups in linear groups over a semilocal ring,” Vestn. Leningr. Univ., No. 13, 16–24 (1976).
Z. I. Borevich and N. A. Vavilov, “Subgroups of the general linear group over a semilocal ring, containing the subgroup of diagonal matrices,” Tr. Mat. Inst. Akad. Nauk SSSR,148, 43–57 (1978).
Z. I. Borevich and N. A. Vavilov, “Determinants in net subgroups,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,114, 37–49 (1982).
Z. I. Borevich, N. A. Vavilov, and V. Narkevich, “Subgroups of the general linear group over a Dedekind ring,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,94, 13–28 (1979).
C. U. Jensen, “Arithmetical rings,” Acta Math. Acad. Sci. Hungar.,17, No. 1–2, 115–123 (1966).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 5–13, 1982.
Rights and permissions
About this article
Cite this article
Borevich, Z.I., Vavilov, N.A. Net determinant over a Bezoutian local ring. J Math Sci 26, 1839–1844 (1984). https://doi.org/10.1007/BF01670567
Issue Date:
DOI: https://doi.org/10.1007/BF01670567