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# Article

 Title: On systems of linear algebraic equations in the Colombeau algebra (English) Author: Ligęza, J. Author: Tvrdý, M. Language: English Journal: Mathematica Bohemica ISSN: 0862-7959 Volume: 124 Issue: 1 Year: 1999 Pages: 1-14 Summary lang: English . Category: math . Summary: 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. (English) Keyword: Colombeau algebra Keyword: system of linear equations Keyword: generalized real numbers MSC: 15A06 MSC: 46F30 MSC: 46F99 idZBL: Zbl 0940.46022 idMR: MR1687437 . Date available: 2009-09-24T21:34:24Z Last updated: 2015-09-15 Stable URL: http://hdl.handle.net/10338.dmlcz/125977 . Reference: [1] Colombeau J. F.: Elementary Introduction to New Generalized Functions.North Holland, Amsterdam, New York, Oxford, 1985. Zbl 0584.46024, MR 0808961 Reference: [2] Ligęza J.: Generalized solutions of boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra.Dissertationes Mathematicae (Different aspect of differentiability) 340 (1995), 183-194. Zbl 0837.34026, MR 1342577 Reference: [3] Mc Cay N.H.: Rings and Ideals.The Carus Mathematical Monographs (Nr. 8), Baltimore, 1948. Reference: [4] Przeworska-Rolewicz D.: Algebraic Analysis.PWN-Polish Scientific Publishers & D. Reidel Publishing Company, Warszawa, 1988. Zbl 0696.47002, MR 0945395 .

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