Abstract:
We prove the local representability and local finite basis property
of varieties of associative rings and algebras over an arbitrary
associative-commutative Noetherian ring Φ.
\Bibitem{Bel10}
\by A.~Ya.~Belov
\paper The local finite basis property and local representability of varieties of associative rings
\jour Izv. Math.
\yr 2010
\vol 74
\issue 1
\pages 1--126
\mathnet{http://mi.mathnet.ru/eng/im1122}
\crossref{https://doi.org/10.1070/IM2010v074n01ABEH002481}
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This publication is cited in the following 27 articles:
Eli Aljadeff, Yakov Karasik, “Semisimple algebras and PI-invariants of finite dimensional algebras”, Alg. Number Th., 18:1 (2024), 133
A. V. Kislitsin, “On Simple Finite-Dimensional Algebras with Infinite Basis of Identities”, Math. Notes, 114:5 (2023), 845–849
Alexei Belov-Kanel, Farrokh Razavinia, Wenchao Zhang, “Centralizers in Free Associative Algebras and Generic Matrices”, Mediterr. J. Math., 20:2 (2023)
Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev, “The Algebraic Classification of Nilpotent Bicommutative Algebras”, Mathematics, 11:3 (2023), 777
Edmond W. H. Lee, Frontiers in Mathematics, Advances in the Theory of Varieties of Semigroups, 2023, 1
A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Jie-Tai, Wenchao Zhang, “Polynomial automorphisms, quantization, and Jacobian conjecture related problems. I. Introduction”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 213, VINITI RAN, M., 2022, 110–144
A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Jie-Tai, Wenchao Zhang, “Polynomial automorphisms, quantization, and Jacobian conjecture related problems. II. Quantization proof of Bergman's centralizer theorem”, Algebra, geometriya i kombinatorika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 214, VINITI RAN, M., 2022, 107–126
A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Dzhi-Tai, Venchao Zheng, “Polinomialnye avtomorfizmy, kvantovanie i zadachi vokrug gipotezy Yakobiana. III. Avtomorfizmy, topologiya popolneniya i approksimatsiya”, Algebra, geometriya i kombinatorika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 215, VINITI RAN, M., 2022, 95–128
A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Dzhi-Tai, Venchao Zheng, “Polinomialnye avtomorfizmy, kvantovanie i zadachi vokrug gipotezy Yakobiana. IV. Approksimatsii polinomialnymi simplektomorfizmami”, Algebra, geometriya, differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 216, VINITI RAN, M., 2022, 153–171
A. M. Elishev, A. Ya. Belov, F. Razavinia, Yu Dzhi-Tai, Venchao Zheng, “Polinomialnye avtomorfizmy, kvantovanie i zadachi vokrug gipotezy Yakobiana. V. Gipoteza Yakobiana i problemy tipa Shpekhta i Bernsaida”, Algebra, geometriya, differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 217, VINITI RAN, M., 2022, 107–137
Jason P. Bell, Peter V. Danchev, “Affine representability and decision procedures for commutativity theorems for rings and algebras”, Isr. J. Math., 249:1 (2022), 121
S. Yu. Antonov, A. V. Antonova, “O kvazimnogochlenakh Kapelli. III”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 21:2 (2021), 142–150
I. A. Reshetnikov, “Kombinatorika slov, faktordinamika i normalnye formy”, Chebyshevskii sb., 22:2 (2021), 202–235
Vesselin Drensky, “Weak polynomial identities and their applications”, Communications in Mathematics, 29:2 (2021), 291
Kanel-Belov A., Yu J.-T., Elishev A., “On the Augmentation Topology of Automorphism Groups of Affine Spaces and Algebras”, Int. J. Algebr. Comput., 28:8, SI (2018), 1449–1485
A. V. Kislitsin, “Simple finite-dimensional algebras without finite basis of identities”, Siberian Math. J., 58:3 (2017), 461–466
G. Deryabina, A. Krasilnikov, “The subalgebra of graded central polynomials of an associative algebra”, J. Algebra, 425 (2015), 313–323
A. V. Kislitsin, “An example of a central simple commutative finite-dimensional algebra with an infinite basis of identities”, Algebra and Logic, 54:3 (2015), 204–210
A. Belov-Kanel, L. Rowen, U. Vishne, “Specht's problem for associative affine algebras over commutative Noetherian rings”, Trans. Amer. Math. Soc., 367:8 (2015), 5553–5596
G. S. Deryabina, A. N. Krasilnikov, “A Non-Finitely-Based Variety of Centrally Metabelian Pointed Groups”, Math. Notes, 95:5 (2014), 743–746
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