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Definition of a net subgroup. / Borevich, Z. I.; Vavilov, N. A.

In: Journal of Soviet Mathematics, Vol. 30, No. 1, 07.1985, p. 1810-1816.

Research output: Contribution to journal › Article › peer-review

Harvard

Borevich, ZI & Vavilov, NA 1985, 'Definition of a net subgroup', Journal of Soviet Mathematics, vol. 30, no. 1, pp. 1810-1816. https://doi.org/10.1007/BF02105093

APA

Borevich, Z. I., & Vavilov, N. A. (1985). Definition of a net subgroup. Journal of Soviet Mathematics, 30(1), 1810-1816. https://doi.org/10.1007/BF02105093

Vancouver

Borevich ZI, Vavilov NA. Definition of a net subgroup. Journal of Soviet Mathematics. 1985 Jul;30(1):1810-1816. https://doi.org/10.1007/BF02105093

Author

Borevich, Z. I. ; Vavilov, N. A. / Definition of a net subgroup. In: Journal of Soviet Mathematics. 1985 ; Vol. 30, No. 1. pp. 1810-1816.

BibTeX

@article{6a6c04f23d744fc0a6f8212ea6fbd7a4,

title = "Definition of a net subgroup",

abstract = "Let Λ be an associative ring with 1 and let b{cyrillic} be a net of ideals in Λ of order n. A net subgroup G(b{cyrillic}) in the general linear group GL(n,Λ) is defined to be the largest subgroup in the multiplicative system e+M(b{cyrillic}), where M (b{cyrillic}) is a subring in the ring of matrices M(n,Λ) associated with b{cyrillic} and e is the unit matrix. This implies that an invertible matrix x, is contained in G(b{cyrillic}) if and only if both the matrices x and x-1 are contained in e+M(b{cyrillic}). The question arises: for which rings is the second of these conditions a consequence of the first?",

author = "Borevich, {Z. I.} and Vavilov, {N. A.}",

year = "1985",

month = jul,

doi = "10.1007/BF02105093",

language = "English",

volume = "30",

pages = "1810--1816",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Definition of a net subgroup

AU - Borevich, Z. I.

AU - Vavilov, N. A.

PY - 1985/7

Y1 - 1985/7

N2 - Let Λ be an associative ring with 1 and let b{cyrillic} be a net of ideals in Λ of order n. A net subgroup G(b{cyrillic}) in the general linear group GL(n,Λ) is defined to be the largest subgroup in the multiplicative system e+M(b{cyrillic}), where M (b{cyrillic}) is a subring in the ring of matrices M(n,Λ) associated with b{cyrillic} and e is the unit matrix. This implies that an invertible matrix x, is contained in G(b{cyrillic}) if and only if both the matrices x and x-1 are contained in e+M(b{cyrillic}). The question arises: for which rings is the second of these conditions a consequence of the first?

AB - Let Λ be an associative ring with 1 and let b{cyrillic} be a net of ideals in Λ of order n. A net subgroup G(b{cyrillic}) in the general linear group GL(n,Λ) is defined to be the largest subgroup in the multiplicative system e+M(b{cyrillic}), where M (b{cyrillic}) is a subring in the ring of matrices M(n,Λ) associated with b{cyrillic} and e is the unit matrix. This implies that an invertible matrix x, is contained in G(b{cyrillic}) if and only if both the matrices x and x-1 are contained in e+M(b{cyrillic}). The question arises: for which rings is the second of these conditions a consequence of the first?

UR - http://www.scopus.com/inward/record.url?scp=0040281465&partnerID=8YFLogxK

U2 - 10.1007/BF02105093

DO - 10.1007/BF02105093

M3 - Article

AN - SCOPUS:0040281465

VL - 30

SP - 1810

EP - 1816

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -

ID: 76484656