Durnev, Valeriĭ Georgievich; Zetkina, Alena Igorevna The problem of solvability of a positive theory of an arbitrary group is algorithmically unsolvable. (Russian. English summary) Zbl 07804914 Chebyshevskiĭ Sb. 24, No. 1(87), 40-49 (2023). Reviewer: Alexander Ivanovich Budkin (Barnaul) MSC: 03D75 20F10 PDFBibTeX XMLCite \textit{V. G. Durnev} and \textit{A. I. Zetkina}, Chebyshevskiĭ Sb. 24, No. 1(87), 40--49 (2023; Zbl 07804914) Full Text: DOI MNR
Durnev, V. G.; Zetkina, A. I. On equations in free monoids and semigroups with restrictions on solutions. (Russian. English summary) Zbl 07724167 Prikl. Diskretn. Mat. 2023, No. 59, 5-19 (2023). MSC: 68-XX 35-XX PDFBibTeX XMLCite \textit{V. G. Durnev} and \textit{A. I. Zetkina}, Prikl. Diskretn. Mat. 2023, No. 59, 5--19 (2023; Zbl 07724167) Full Text: DOI MNR
Durnev, V. G.; Zetkina, O. V.; Zetkina, A. I. Algorithmic undecidability of compatibility problem for equations in free groups: explicit equations with one commutator-type constraint. (English) Zbl 1462.20014 J. Algebra 570, 452-469 (2021). Reviewer: Egle Bettio (Venezia) MSC: 20F10 20E05 20F18 20F05 PDFBibTeX XMLCite \textit{V. G. Durnev} et al., J. Algebra 570, 452--469 (2021; Zbl 1462.20014) Full Text: DOI
Durnev, Valeriĭ Georgievich; Zetkina, Oksana Valer’evna; Zetkina, Alena Igor’evna On elementary theories of algebraically closed groups. (Russian. English summary) Zbl 1455.03045 Chebyshevskiĭ Sb. 21, No. 1(73), 165-178 (2020). MSC: 03C60 20F10 PDFBibTeX XMLCite \textit{V. G. Durnev} et al., Chebyshevskiĭ Sb. 21, No. 1(73), 165--178 (2020; Zbl 1455.03045) Full Text: MNR
Durnev, V. G.; Zetkina, O. V. Some of the results obtained in the Yaroslavl branch algebraic school of M. D. Grindlinger. (Russian. English summary) Zbl 1434.20003 Chebyshevskiĭ Sb. 15, No. 4(52), 5-31 (2014). MSC: 20-03 01A60 01A72 20E05 20M05 PDFBibTeX XMLCite \textit{V. G. Durnev} and \textit{O. V. Zetkina}, Chebyshevskiĭ Sb. 15, No. 4(52), 5--31 (2014; Zbl 1434.20003) Full Text: MNR
Durnev, V. G.; Zetkina, O. V. On equations in free semigroups with certain constraints on their solutions. (English. Russian original) Zbl 1183.20060 J. Math. Sci., New York 158, No. 5, 671-676 (2009); translation from Zap. Nauchn. Semin. POMI 358, 120-129 (2008). MSC: 20M05 03D35 20F70 PDFBibTeX XMLCite \textit{V. G. Durnev} and \textit{O. V. Zetkina}, J. Math. Sci., New York 158, No. 5, 671--676 (2009; Zbl 1183.20060); translation from Zap. Nauchn. Semin. POMI 358, 120--129 (2008) Full Text: DOI
Durnev, V. G. Undecidability of the positive \(\forall\exists^ 3\)-theory of a free semigroup. (English. Russian original) Zbl 0853.20035 Sib. Math. J. 36, No. 5, 917-929 (1995); translation from Sib. Mat. Zh. 36, No. 5, 1067-1080 (1995). MSC: 20M05 03D35 PDFBibTeX XMLCite \textit{V. G. Durnev}, Sib. Math. J. 36, No. 5, 917--929 (1995; Zbl 0853.20035); translation from Sib. Mat. Zh. 36, No. 5, 1067--1080 (1995) Full Text: DOI
Durnev, V. G. Generalization of problem 9.25 from “The Kourovka notebook”. (English. Russian original) Zbl 0702.20023 Math. Notes 47, No. 2, 117-121 (1990); translation from Mat. Zametki 47, No. 2, 15-19 (1990). MSC: 20F10 20E05 PDFBibTeX XMLCite \textit{V. G. Durnev}, Math. Notes 47, No. 2, 117--121 (1990; Zbl 0702.20023); translation from Mat. Zametki 47, No. 2, 15--19 (1990) Full Text: DOI