Systems of equations and lattices of congruences of universal algebras
Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 4, pp. 109-144
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We investigate the dependence of properties of systems of equations over the universal algebras on the properties of lattices of congruences of these algebras. Our main result is the description of conditions on the lattice of congruences under which it is possible to construct a Gauss-like algorithm of solution of systems of equations.
[1] Asanov M. O., Baranskii V. A., Rasin V. V., Diskretnaya matematika: Grafy, matroidy, algoritmy, NITs “RKhD”, Izhevsk, 2001
[2] Balakin G. V., “Vvedenie v teoriyu sluchainykh uravnenii”, Trudy po diskretnoi matematike, 1, TVP, M., 1997, 1–18 | MR | Zbl
[3] Grettser G., Obschaya teoriya reshetok, Mir, M., 1982 | MR
[4] Kon P., Universalnaya algebra, Mir, M., 1968 | MR
[5] Kurosh A. G., Lektsii po obschei algebre, Nauka, M., 1973 | MR