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Volume 57 >>> № 6 NOVEMBER — DECEMBER 2021

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UDC 004.822

S. Kryvyi¹

¹ Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

ALGORITHMS FOR SOLVIG LINEAR EQUATIONS OVER ASSOCIATIVE
RINGS WITH UNITY ELEMENT

Abstract. The author proposes algorithms for solving linear equations and systems of such equations in associative non-commutative rings with unity under the condition that all the coefficients in the equations are divisors of unity. The basic concepts of ring theory and examples of operation of the proposed algorithms are provided. The complexity of the algorithms depends on the properties of elements of the ring over which the equations and systems of equations are considered.

Keywords: linear equation, non-commutative ring, divisor of unit, algorithm.

FULL TEXT

REFERENCES

Kryvyi S.L. Algorithms for solving systems of linear Diophantine equations in a residue ring. Kibernetika i sistemnyi analiz. 2007. N 6. P. 27–40.

Kryvyi S.L. Algorithms for constructing a basis for the set of solutions of systems of linear Diophantine equations in the ring of integers. Kibernetika i sistemnyi analiz. 2009. N 6. P. 36–41.

A.I. Kostrikin Introduction to Algebra (Part 2). Moscow: Fizmatlit, 2004. 272 p.

Skobelev V.V. Automata on algebraic structures. Research models and methods. Donetsk: IPM NASU, 2013. 307 p.

Bockmayr A., Weispfenning V. Solving numerical constraints. Handbook of Automated Reasoning. 2001. Ch. 12. P. 753–842.

UDC 004.822

ALGORITHMS FOR SOLVIG LINEAR EQUATIONS OVER ASSOCIATIVE RINGS WITH UNITY ELEMENT

REFERENCES

ALGORITHMS FOR SOLVIG LINEAR EQUATIONS OVER ASSOCIATIVE
RINGS WITH UNITY ELEMENT