Geodesic
Direct powers of algebraic structures and equations
Prikladnaâ diskretnaâ matematika, no. 4 (2022), pp. 31-39.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study systems of equations over graphs, posets and matroids. We give the criteria when a direct power of such algebraic structures is equationally Noetherian. Moreover, we prove that any direct power of any finite algebraic structure is weakly equationally Noetherian.
Keywords: graphs, matroids, finite algebraic structures, direct powers, equationally Noetherian algebraic structures. 
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     title = {Direct powers of algebraic structures and equations},
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     url = {http://geodesic.mathdoc.fr/item/PDM_2022_4_a3/}
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A. Shevlyakov. Direct powers of algebraic structures and equations. Prikladnaâ diskretnaâ matematika, no. 4 (2022), pp. 31-39. http://geodesic.mathdoc.fr/item/PDM_2022_4_a3/

[1] Daniyarova E. Yu., Myasnikov A. G., and Remeslennikov V. N., “Unification theorems in algebraic geometry”, Algebra Discr. Math., 1 (2008), 80–112 | MR

[2] Daniyarova E. Yu., Myasnikov A. G., and Remeslennikov V. N., “Algebraic geometry over algebraic structures, II: Foundations”, J. Math. Sci., 183 (2012), 389–416 | DOI | MR

[3] Daniyarova E. Yu., Myasnikov A. G., and Remeslennikov V. N., “Algebraic geometry over algebraic structures, III: Equationally noetherian property and compactness”, Southern Asian Bull. Math., 35:1 (2011), 35–68 | MR

[4] Shevlyakov A. N. and Shahryari M., “Direct products, varieties, and compactness conditions”, Groups Complexity Cryptology, 9:2 (2017), 159–166 | MR