# On systems of linear algebraic equations in the Colombeau algebra

Mathematica Bohemica (1999)

- Volume: 124, Issue: 1, page 1-14
- ISSN: 0862-7959

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topLigęza, Jan, and Tvrdý, Milan. "On systems of linear algebraic equations in the Colombeau algebra." Mathematica Bohemica 124.1 (1999): 1-14. <http://eudml.org/doc/248461>.

@article{Ligęza1999,

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 $\overline\{\mathbb \{R\}\}$ of generalized real numbers. It is worth mentioning that the algebra $\overline\{\mathbb \{R\}\}$ is not a field.},

author = {Ligęza, Jan, Tvrdý, Milan},

journal = {Mathematica Bohemica},

keywords = {Colombeau algebra; system of linear equations; generalized real numbers; Colombeau algebra; system of linear equations; generalized real numbers},

language = {eng},

number = {1},

pages = {1-14},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On systems of linear algebraic equations in the Colombeau algebra},

url = {http://eudml.org/doc/248461},

volume = {124},

year = {1999},

}

TY - JOUR

AU - Ligęza, Jan

AU - Tvrdý, Milan

TI - On systems of linear algebraic equations in the Colombeau algebra

JO - Mathematica Bohemica

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 124

IS - 1

SP - 1

EP - 14

AB - 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 $\overline{\mathbb {R}}$ of generalized real numbers. It is worth mentioning that the algebra $\overline{\mathbb {R}}$ is not a field.

LA - eng

KW - Colombeau algebra; system of linear equations; generalized real numbers; Colombeau algebra; system of linear equations; generalized real numbers

UR - http://eudml.org/doc/248461

ER -

## References

top- Colombeau J. F., Elementary Introduction to New Generalized Functions, North Holland, Amsterdam, New York, Oxford, 1985. (1985) Zbl0584.46024MR0808961
- 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. (1995) Zbl0837.34026MR1342577
- Mc Cay N.H., Rings and Ideals, The Carus Mathematical Monographs (Nr. 8), Baltimore, 1948. (1948)
- Przeworska-Rolewicz D., Algebraic Analysis, PWN-Polish Scientific Publishers & D. Reidel Publishing Company, Warszawa, 1988. (1988) Zbl0696.47002MR0945395

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