On pairs of matrices generating matrix rings and their presentations

B.V. Petrenko; S.N. Sidki

doi:10.1016/J.JALGEBRA.2006.08.011

On pairs of matrices generating matrix rings and their presentations

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

Original language	American English
Journal	Journal of Algebra
Volume	310
DOIs	https://doi.org/10.1016/J.JALGEBRA.2006.08.011
State	Published - Apr 1 2007
Externally published	Yes

Disciplines

Mathematics
Discrete Mathematics and Combinatorics

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@article{283791ed78bc4198901dbd746699186c,

title = "On pairs of matrices generating matrix rings and their presentations",

author = "B.V. Petrenko and S.N. Sidki",

note = "By B.V. Petrenko and S.N. Sidki AbstractLet Mn(Z) be the ring of n-by-n matrices with integral entries, and n⩾2. This paper studies the set Gn(Z) of pairs (A,B)∈Mn(Z)2 generating Mn(Z) as a ring. We use several presentations of Mn(Z) with generators X=∑i=1nEi+1,i and Y=E11 to obtain the following consequences.(1)Let k⩾1.",

year = "2007",

month = apr,

day = "1",

doi = "10.1016/J.JALGEBRA.2006.08.011",

language = "American English",

volume = "310",

journal = "Journal of Algebra",

}

TY - JOUR

T1 - On pairs of matrices generating matrix rings and their presentations

AU - Petrenko, B.V.

AU - Sidki, S.N.

N1 - By B.V. Petrenko and S.N. Sidki AbstractLet Mn(Z) be the ring of n-by-n matrices with integral entries, and n⩾2. This paper studies the set Gn(Z) of pairs (A,B)∈Mn(Z)2 generating Mn(Z) as a ring. We use several presentations of Mn(Z) with generators X=∑i=1nEi+1,i and Y=E11 to obtain the following consequences.(1)Let k⩾1.

PY - 2007/4/1

Y1 - 2007/4/1

UR - https://core.ac.uk/display/82303301

U2 - 10.1016/J.JALGEBRA.2006.08.011

DO - 10.1016/J.JALGEBRA.2006.08.011

M3 - Article

VL - 310

JO - Journal of Algebra

JF - Journal of Algebra

ER -

On pairs of matrices generating matrix rings and their presentations

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