MATHEMATICA BOHEMICA, Vol. 124, No. 1, pp. 1-14, 1999

# On systems of linear algebraic equations in the Colombeau algebra

## J. Ligeza, M. Tvrdy

Jan Ligeza, Uniwersytet Slaski, Instytut Matematyki, ul. Bankowa 14, 40-007 Katowice, Poland, e-mail: ligeza@ux2.math.us.edu.pl;
Milan Tvrdy, Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: tvrdy@math.cas.cz

Abstract: From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra $\overline{\Bbb R}$ of generalized real numbers. It is worth mentioning that the algebra $\overline{\Bbb R}$ is not a field.

Keywords: Colombeau algebra, system of linear equations

Classification (MSC 1991): 46F99, 15A06

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