Geodesic
On a class of 3-good formal matrix rings
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 67 (2020), pp. 55-62

Voir la notice de l'article provenant de la source Math-Net.Ru

We study formal matrix rings with values in a given ring and with a matrix of factors consisting of 0 and 1. Under the indicated restrictions, the formal matrix ring can be represented as a splitting extension of one of its nilpotent ideal using the product of ordinary matrix rings, and the question of the invertibility of the formal matrix is reduced to to the question of the invertibility of ordinary matrices over a ring. Under some additional conditions imposed on the matrix of factors, it is possible to use the well-known Henriksen theorem and prove that every element of a formal matrix ring is the sum of three invertible elements of this ring. Finally, we give examples of such formal matrix rings of orders 4 and 5.
Keywords: ring, good ring, formal matrix ring. 
@article{VTGU_2020_67_a4,
     author = {T. D. Norbosambuev and E. A. Timoshenko},
     title = {On a class of 3-good formal matrix rings},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {55--62},
     publisher = {mathdoc},
     number = {67},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2020_67_a4/}
}
TY  - JOUR
AU  - T. D. Norbosambuev
AU  - E. A. Timoshenko
TI  - On a class of 3-good formal matrix rings
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2020
SP  - 55
EP  - 62
IS  - 67
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTGU_2020_67_a4/
LA  - ru
ID  - VTGU_2020_67_a4
ER  - 
%0 Journal Article
%A T. D. Norbosambuev
%A E. A. Timoshenko
%T On a class of 3-good formal matrix rings
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2020
%P 55-62
%N 67
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTGU_2020_67_a4/
%G ru
%F VTGU_2020_67_a4
T. D. Norbosambuev; E. A. Timoshenko. On a class of 3-good formal matrix rings. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 67 (2020), pp. 55-62. http://geodesic.mathdoc.fr/item/VTGU_2020_67_a4/