An inverse matrix of an upper triangular matrix can be lower triangular

• Autorzy: Waldemar Hołubowski
• Języki publikacji: EN

Abstrakty

EN

In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.

Słowa kluczowe

EN

upper tringular invertible matrix; group of matrices; Dedekind-finite ring

Kategorie tematyczne

• 20H25: Other matrix groups over rings

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2002
• Tom: 22
• Numer: 2
• Strony: 161-166

Daty

wydano

2002

Twórcy

autor

Waldemar Hołubowski

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-101 Gliwice, Poland

Bibliografia

• [1] H. Anton and C. Rorres, Elementary Linear algebra. Applications version, 8-th edition, J. Wiley, New York 2000.
• [2] C.M. Bang, A condition for two matrices to be inverses of each other, Amer. Math. Monthly (1974), 764-767.
• [3] I.D. Ion and M. Constantinescu, Sur les anneaux Dedekind-finis, Italian J. Pure Appl. Math. 7 (2000), 19-25.
• [4] N. Jacobson, Structure of rings, Amer. Math. Soc., RI, Providence 1956.
• [5] M.I. Kargapolov and Yu. I. Merzlakov, Fundamentals of the theory of groups, Springer-Verlag, New York 1979.
• [6] D.J.S. Robinson, A course in the theory of groups, Springer-Verlag, New York 1982.
• [7] A. Stepanov and N. Vavilov, Decomposition of transvections: a theme with variations, K- Theory 19 (2000), 109-153.

Identyfikatory

DOI

10.7151/dmgaa.1055