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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 5, Pages 201–214 (Mi izv8295)  

This article is cited in 5 scientific papers (total in 5 papers)

Hilbert's Nullstellensatz in algebraic geometry over rigid soluble groups

N. S. Romanovskiy

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We discuss the problem of the possible form of an analogue of the classical Nullstellensatz of Hilbert in algebraic geometry over a suitable class of groups and prove such an analogue in the class of rigid soluble groups.

Keywords: group, soluble group, algebraic geometry.

Funding Agency Grant Number
Russian Science Foundation 14-21-00065
The research was completed with the support of a grant from the Russian Science Foundation (project no. 14-21-00065).


DOI: https://doi.org/10.4213/im8295

Full text: PDF file (470 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:5, 1051–1063

Bibliographic databases:

UDC: 512.5
MSC: Primary 14A99; Secondary 03C05, 08B05, 20E99
Received: 10.09.2014

Citation: N. S. Romanovskiy, “Hilbert's Nullstellensatz in algebraic geometry over rigid soluble groups”, Izv. RAN. Ser. Mat., 79:5 (2015), 201–214; Izv. Math., 79:5 (2015), 1051–1063

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. S. Romanovskii, “Partially divisible completions of rigid metabelian pro-$p$-groups”, Algebra and Logic, 55:5 (2016), 376–386  mathnet  crossref  crossref  isi
    2. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VI. Geometric equivalence”, Algebra and Logic, 56:4 (2017), 281–294  mathnet  crossref  crossref  isi
    3. N. S. Romanovskii, “Generalized rigid groups: definitions, basic properties, and problems”, Siberian Math. J., 59:4 (2018), 705–709  mathnet  crossref  crossref  isi  elib
    4. A. G. Myasnikov, N. S. Romanovskii, “Characterization of finitely generated groups by types”, Int. J. Algebr. Comput., 28:8, SI (2018), 1613–1632  crossref  mathscinet  zmath  isi
    5. N. S. Romanovskii, “Generalized rigid metabelian groups”, Siberian Math. J., 60:1 (2019), 148–152  mathnet  crossref  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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