Geodesic
Direct powers of algebraic structures and equations
Prikladnaâ diskretnaâ matematika, no. 4 (2022), pp. 31-39 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{PDM_2022_4_a3,
     author = {A. Shevlyakov},
     title = {Direct powers of algebraic structures and equations},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {31--39},
     year = {2022},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PDM_2022_4_a3/}
}
TY  - JOUR
AU  - A. Shevlyakov
TI  - Direct powers of algebraic structures and equations
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2022
SP  - 31
EP  - 39
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/PDM_2022_4_a3/
LA  - en
ID  - PDM_2022_4_a3
ER  - 
%0 Journal Article
%A A. Shevlyakov
%T Direct powers of algebraic structures and equations
%J Prikladnaâ diskretnaâ matematika
%D 2022
%P 31-39
%N 4
%U http://geodesic.mathdoc.fr/item/PDM_2022_4_a3/
%G en
%F PDM_2022_4_a3
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