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Russian Academy of Sciences. Izvestiya Mathematics, 1993, Volume 41, Issue 2, Pages 351–365
DOI: https://doi.org/10.1070/IM1993v041n02ABEH002265 (Mi im920) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Generalized and local Jacobian problems

Vik. S. Kulikov

Moscow State University of Railway Communications
English version PDF (744 kB) Citations (8) Russian version article
References:
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DOI: https://doi.org/10.1070/IM1993v041n02ABEH002265
Abstract: In this paper we construct a counterexample to the generalized Jacobian problem and give a positive solution of the local analogue of the classical Jacobian problem. We study the relationship between the classical Jacobian problem and certain problems connected with the algebra of differentiations of the ring of polynomials.
Received: 23.04.1991
Bibliographic databases:
Document Type: Article
UDC: 512.7+515.1
MSC: 12H05, 14E20, 14E22, 20F34, 35F10, 57M05
Language: English
Original paper language: Russian
Citation: Vik. S. Kulikov, “Generalized and local Jacobian problems”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 351–365
Citation in format AMSBIB
\Bibitem{Kul92}
\by Vik.~S.~Kulikov
\paper Generalized and local Jacobian problems
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 2
\pages 351--365
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\crossref{https://doi.org/10.1070/IM1993v041n02ABEH002265}
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..351K}
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    • This publication is cited in the following 8 articles:
    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  mathnet  crossref
    2. 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  mathnet  crossref
    3. 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  mathnet  crossref
    4. 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  mathnet  crossref
    5. 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  mathnet  crossref
    6. V. V. Starkov, “The Jacobian conjecture: structure of Keller mappings”, Probl. anal. Issues Anal., 8(26):3 (2019), 152–165  mathnet  crossref  elib
    7. V. V. Starkov, “Structure of Keller mappings, two-dimensional case”, Probl. anal. Issues Anal., 6(24):1 (2017), 68–81  mathnet  crossref  elib
    8. V. V. Starkov, “Jacobian conjecture, two-dimensional case”, Probl. anal. Issues Anal., 5(23):2 (2016), 69–78  mathnet  crossref  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:78
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