Amaglobeli, M. G.; Miasnikov, A. G.; Remeslennikov, V. N. Description of coordinate groups of irreducible algebraic sets over free 2-nilpotent groups. (English. Russian original) Zbl 1520.20097 Dokl. Math. 105, No. 2, 68-70 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 503, 23-25 (2022). Reviewer: Egle Bettio (Venezia) MSC: 20F70 20F18 14A22 PDFBibTeX XMLCite \textit{M. G. Amaglobeli} et al., Dokl. Math. 105, No. 2, 68--70 (2022; Zbl 1520.20097); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 503, 23--25 (2022) Full Text: DOI
Chen, Haimiao Solving the isomorphism problems for two families of parafree groups. (English) Zbl 07373708 J. Algebra 585, 616-636 (2021). MSC: 20-XX 55N25 20F14 14F35 20E05 20E26 20J05 14M30 PDFBibTeX XMLCite \textit{H. Chen}, J. Algebra 585, 616--636 (2021; Zbl 07373708) Full Text: DOI arXiv
Shahryari, Mohammad; Tayyebi, Javad On the equationally Artinian groups. (English) Zbl 07334117 J. Sib. Fed. Univ., Math. Phys. 13, No. 5, 583-595 (2020). MSC: 20Exx 14Axx PDFBibTeX XMLCite \textit{M. Shahryari} and \textit{J. Tayyebi}, J. Sib. Fed. Univ., Math. Phys. 13, No. 5, 583--595 (2020; Zbl 07334117) Full Text: DOI arXiv MNR
Nouri, Mahdiyeh Algebraic geometry over Heyting algebras. (English) Zbl 07334101 J. Sib. Fed. Univ., Math. Phys. 13, No. 4, 414-421 (2020). MSC: 20Exx 14Axx PDFBibTeX XMLCite \textit{M. Nouri}, J. Sib. Fed. Univ., Math. Phys. 13, No. 4, 414--421 (2020; Zbl 07334101) Full Text: DOI MNR
Jones, Gareth Aneurin Automorphism groups of maps, hypermaps and dessins. (English) Zbl 1441.20003 Art Discrete Appl. Math. 3, No. 1, Paper No. P1.06, 14 p. (2020). MSC: 20B25 20B27 05C10 14H57 52B15 57M10 PDFBibTeX XMLCite \textit{G. A. Jones}, Art Discrete Appl. Math. 3, No. 1, Paper No. P1.06, 14 p. (2020; Zbl 1441.20003) Full Text: DOI arXiv
Koberda, Thomas; Suciu, Alexander I. Residually finite rationally \(p\) groups. (English) Zbl 1477.20057 Commun. Contemp. Math. 22, No. 3, Article ID 1950016, 44 p. (2020). MSC: 20E26 14H50 20F65 52C35 55N25 57M10 57K30 PDFBibTeX XMLCite \textit{T. Koberda} and \textit{A. I. Suciu}, Commun. Contemp. Math. 22, No. 3, Article ID 1950016, 44 p. (2020; Zbl 1477.20057) Full Text: DOI arXiv
Shevlyakov, Artem N. On algebraic geometry over completely simple semigroups. (English) Zbl 1443.20087 Int. J. Group Theory 8, No. 2, 1-10 (2019). MSC: 20M05 20M07 20M99 14A99 PDFBibTeX XMLCite \textit{A. N. Shevlyakov}, Int. J. Group Theory 8, No. 2, 1--10 (2019; Zbl 1443.20087) Full Text: DOI
Shevlyakov, Artem N. On group automorphisms in universal algebraic geometry. (English) Zbl 1435.20029 Groups Complex. Cryptol. 11, No. 2, 115-121 (2019). MSC: 20D45 20E36 20F70 14A99 08A99 PDFBibTeX XMLCite \textit{A. N. Shevlyakov}, Groups Complex. Cryptol. 11, No. 2, 115--121 (2019; Zbl 1435.20029) Full Text: DOI arXiv
Daniyarova, E. Y. U.; Myasnikov, A. G.; Remeslennikov, V. N. Algebraic geometry over algebraic structures. IX: Principal universal classes and dis-limits. (English. Russian original) Zbl 1429.08007 Algebra Logic 57, No. 6, 414-428 (2019); translation from Algebra Logika 57, No. 6, 639-661 (2018). MSC: 08A99 14A22 03C05 PDFBibTeX XMLCite \textit{E. Y. U. Daniyarova} et al., Algebra Logic 57, No. 6, 414--428 (2019; Zbl 1429.08007); translation from Algebra Logika 57, No. 6, 639--661 (2018) Full Text: DOI
Stover, Matthew Lattices in \(\operatorname{PU}(n,1)\) that are not profinitely rigid. (English) Zbl 1453.20040 Proc. Am. Math. Soc. 147, No. 12, 5055-5062 (2019). MSC: 20E18 20H10 11G18 14G35 11F06 20F67 PDFBibTeX XMLCite \textit{M. Stover}, Proc. Am. Math. Soc. 147, No. 12, 5055--5062 (2019; Zbl 1453.20040) Full Text: DOI arXiv
Plotkin, Boris Seven lectures on universal algebraic geometry. (English) Zbl 1503.08003 Plotkin, Eugene (ed.), Groups, algebras and identities. Research workshop of the Israel Science Foundation ‘Groups, algebras and identities’. In honor of Boris Plotkin’s 90th birthday, Bar-Ilan University and The Hebrew University of Jerusalem, Israel, March 20–24, 2016. Providence, RI: American Mathematical Society (AMS); Ramat Gan: Bar-Ilan University. Contemp. Math. 726, 143-215 (2019). MSC: 08B99 08C05 03G15 14A99 08-02 PDFBibTeX XMLCite \textit{B. Plotkin}, Contemp. Math. 726, 143--215 (2019; Zbl 1503.08003) Full Text: DOI arXiv
Lipyanski, R. On the Zariski topology of \(\Omega\)-groups. (English) Zbl 1423.16028 Plotkin, Eugene (ed.), Groups, algebras and identities. Research workshop of the Israel Science Foundation ‘Groups, algebras and identities’. In honor of Boris Plotkin’s 90th birthday, Bar-Ilan University and The Hebrew University of Jerusalem, Israel, March 20–24, 2016. Providence, RI: American Mathematical Society (AMS); Ramat Gan: Bar-Ilan University. Contemp. Math. 726, 135-142 (2019). MSC: 16S38 14A22 08B20 PDFBibTeX XMLCite \textit{R. Lipyanski}, Contemp. Math. 726, 135--142 (2019; Zbl 1423.16028) Full Text: DOI arXiv Link
Lipyanski, R. Geometric equivalence of \(\pi\)-torsion-free nilpotent groups. (English) Zbl 1466.20030 Plotkin, Eugene (ed.), Groups, algebras and identities. Research workshop of the Israel Science Foundation ‘Groups, algebras and identities’. In honor of Boris Plotkin’s 90th birthday, Bar-Ilan University and The Hebrew University of Jerusalem, Israel, March 20–24, 2016. Providence, RI: American Mathematical Society (AMS); Ramat Gan: Bar-Ilan University. Contemp. Math. 726, 123-133 (2019). MSC: 20F18 20D15 14A22 14A20 20E10 PDFBibTeX XMLCite \textit{R. Lipyanski}, Contemp. Math. 726, 123--133 (2019; Zbl 1466.20030) Full Text: DOI arXiv
Di Nola, Antonio; Lenzi, Giacomo; Vitale, Gaetano Algebraic geometry for \(\ell \)-groups. (English) Zbl 1472.06023 Algebra Univers. 79, No. 3, Paper No. 64, 24 p. (2018). MSC: 06F20 03G25 08C05 14A99 PDFBibTeX XMLCite \textit{A. Di Nola} et al., Algebra Univers. 79, No. 3, Paper No. 64, 24 p. (2018; Zbl 1472.06023) Full Text: DOI
Shahryari, Mohammad Algebraic sets with fully characteristic radicals. (English) Zbl 07325352 J. Sib. Fed. Univ., Math. Phys. 10, No. 3, 293-297 (2017). MSC: 08A99 03C05 14A22 PDFBibTeX XMLCite \textit{M. Shahryari}, J. Sib. Fed. Univ., Math. Phys. 10, No. 3, 293--297 (2017; Zbl 07325352) Full Text: DOI arXiv MNR
Shahryari, Mohammad; Shevlyakov, Artem Direct products, varieties, and compactness conditions. (English) Zbl 1401.08003 Groups Complex. Cryptol. 9, No. 2, 159-166 (2017). MSC: 08B25 08A45 03C05 14A99 PDFBibTeX XMLCite \textit{M. Shahryari} and \textit{A. Shevlyakov}, Groups Complex. Cryptol. 9, No. 2, 159--166 (2017; Zbl 1401.08003) Full Text: DOI arXiv
Khodabandeh, H.; Shahryari, M. Equations in polyadic groups. (English) Zbl 1431.20043 Commun. Algebra 45, No. 3, 1227-1238 (2017). Reviewer: Bijan Davvaz (Yazd) MSC: 20N15 20F70 08A05 14L10 PDFBibTeX XMLCite \textit{H. Khodabandeh} and \textit{M. Shahryari}, Commun. Algebra 45, No. 3, 1227--1238 (2017; Zbl 1431.20043) Full Text: DOI arXiv
Modabberi, P.; Shahryari, M. Compactness conditions in universal algebraic geometry. (English. Russian original) Zbl 1367.08002 Algebra Logic 55, No. 2, 146-172 (2016); translation from Algebra Logika 55, No. 2, 219-256 (2016). MSC: 08A45 14A20 PDFBibTeX XMLCite \textit{P. Modabberi} and \textit{M. Shahryari}, Algebra Logic 55, No. 2, 146--172 (2016; Zbl 1367.08002); translation from Algebra Logika 55, No. 2, 219--256 (2016) Full Text: DOI arXiv
Benyash-Krivets, V. V.; Govorushko, I. O. Representation and character varieties of the Baumslag-Solitar groups. (English. Russian original) Zbl 1386.20004 Proc. Steklov Inst. Math. 292, 20-36 (2016); translation from Tr. Mat. Inst. Steklova 292, 26-42 (2016). Reviewer: Clément Guérin (Esch-sur-Alzette) MSC: 20C15 14D20 20G05 14C35 PDFBibTeX XMLCite \textit{V. V. Benyash-Krivets} and \textit{I. O. Govorushko}, Proc. Steklov Inst. Math. 292, 20--36 (2016; Zbl 1386.20004); translation from Tr. Mat. Inst. Steklova 292, 26--42 (2016) Full Text: DOI
Benyash-Krivets, V. V.; Govorushko, I. O. Representation varieties of finite index subgroups of Baumslag-Solitar groups. (Russian. English summary) Zbl 1459.20002 Tr. Inst. Mat., Minsk 23, No. 2, 24-28 (2015). MSC: 20C15 14D20 20G05 14C35 PDFBibTeX XMLCite \textit{V. V. Benyash-Krivets} and \textit{I. O. Govorushko}, Tr. Inst. Mat., Minsk 23, No. 2, 24--28 (2015; Zbl 1459.20002) Full Text: MNR
Borovoi, Mikhail; Cornulier, Yves Conjugate complex homogeneous spaces with non-isomorphic fundamental groups. (Espaces homogènes complexes conjugués avec groupes fondamentaux non isomorphes.) (English. Abridged French version) Zbl 1349.14159 C. R., Math., Acad. Sci. Paris 353, No. 11, 1001-1005 (2015). MSC: 14M17 14F35 22E40 55Q05 PDFBibTeX XMLCite \textit{M. Borovoi} and \textit{Y. Cornulier}, C. R., Math., Acad. Sci. Paris 353, No. 11, 1001--1005 (2015; Zbl 1349.14159) Full Text: DOI arXiv
Afanas’eva, S. G. The coordinate group of an affine space over a rigid metabelian pro-\(p\)-group. (English. Russian original) Zbl 1315.20042 Algebra Logic 53, No. 3, 187-190 (2014); translation from Algebra Logika 53, No. 3, 295-299 (2014). MSC: 20F70 20E18 20F16 14R10 PDFBibTeX XMLCite \textit{S. G. Afanas'eva}, Algebra Logic 53, No. 3, 187--190 (2014; Zbl 1315.20042); translation from Algebra Logika 53, No. 3, 295--299 (2014) Full Text: DOI
Belluce, Lawrence P.; Di Nola, Antonio; Lenzi, Giacomo Algebraic geometry for MV-algebras. (English) Zbl 1353.06007 J. Symb. Log. 79, No. 4, 1061-1091 (2014). MSC: 06D35 14A20 03G25 PDFBibTeX XMLCite \textit{L. P. Belluce} et al., J. Symb. Log. 79, No. 4, 1061--1091 (2014; Zbl 1353.06007) Full Text: DOI Link
Cornulier, Yves Sofic profile and computability of Cremona groups. (English) Zbl 1300.14015 Mich. Math. J. 62, No. 4, 823-841 (2013). Reviewer: Iván Pan (Montevideo) MSC: 14E07 PDFBibTeX XMLCite \textit{Y. Cornulier}, Mich. Math. J. 62, No. 4, 823--841 (2013; Zbl 1300.14015) Full Text: DOI arXiv Euclid
Plotkin, B. I. Isotyped algebras. (English. Russian original) Zbl 1361.03067 Proc. Steklov Inst. Math. 278, Suppl. 1, S91-S115 (2012); translation from Sovrem. Probl. Mat. 15, 40-66 (2011). MSC: 03G25 08B99 08C05 14A99 PDFBibTeX XMLCite \textit{B. I. Plotkin}, Proc. Steklov Inst. Math. 278, S91--S115 (2012; Zbl 1361.03067); translation from Sovrem. Probl. Mat. 15, 40--66 (2011) Full Text: DOI
Daniyarova, E. Yu.; Myasnikov, A. G.; Remeslennikov, V. N. Algebraic geometry over algebraic structures. II: Foundations. (English. Russian original) Zbl 1256.03037 J. Math. Sci., New York 185, No. 3, 389-416 (2012); translation from Fundam. Prikl. Mat. 17, No. 1, 65-106 (2012). MSC: 03C05 03C60 08Bxx 08Cxx 14A99 PDFBibTeX XMLCite \textit{E. Yu. Daniyarova} et al., J. Math. Sci., New York 185, No. 3, 389--416 (2012; Zbl 1256.03037); translation from Fundam. Prikl. Mat. 17, No. 1, 65--106 (2012) Full Text: DOI arXiv
Daniyarova, E. Yu.; Myasnikov, A. G.; Remeslennikov, V. N. Algebraic geometry over algebraic structures. V: The case of arbitrary signature. (English. Russian original) Zbl 1255.08001 Algebra Logic 51, No. 1, 28-40 (2012); translation from Algebra Logika 51, No. 1, 41-60 (2012). MSC: 08A99 03C05 14A22 PDFBibTeX XMLCite \textit{E. Yu. Daniyarova} et al., Algebra Logic 51, No. 1, 28--40 (2012; Zbl 1255.08001); translation from Algebra Logika 51, No. 1, 41--60 (2012) Full Text: DOI
Pinus, A. G. Implicit algebraic geometry on categories of universal algebras. (English. Russian original) Zbl 1263.18002 Russ. Math. 56, No. 5, 34-38 (2012); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012, No. 5, 40-45 (2012). Reviewer: Michel Hébert (Cairo) MSC: 18C05 14A99 08C05 08A99 PDFBibTeX XMLCite \textit{A. G. Pinus}, Russ. Math. 56, No. 5, 34--38 (2012; Zbl 1263.18002); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012, No. 5, 40--45 (2012) Full Text: DOI
Romanovskiĭ, N. S. Coproducts of rigid groups. (English. Russian original) Zbl 1236.20039 Algebra Logic 49, No. 6, 539-550 (2011); translation from Algebra Logika 49, No. 6, 803-818 (2010). MSC: 20F14 20F16 20E22 14A22 20F70 PDFBibTeX XMLCite \textit{N. S. Romanovskiĭ}, Algebra Logic 49, No. 6, 539--550 (2011; Zbl 1236.20039); translation from Algebra Logika 49, No. 6, 803--818 (2010) Full Text: DOI
Daniyarova, É. Yu.; Myasnikov, A. G.; Remeslennikov, V. N. Algebraic geometry over algebraic structures. IV: Equational domains and codomains. (English. Russian original) Zbl 1245.08005 Algebra Logic 49, No. 6, 483-508 (2011); translation from Algebra Logika 49, No. 6, 715-756 (2010). MSC: 08A99 03C05 14A22 PDFBibTeX XMLCite \textit{É. Yu. Daniyarova} et al., Algebra Logic 49, No. 6, 483--508 (2011; Zbl 1245.08005); translation from Algebra Logika 49, No. 6, 715--756 (2010) Full Text: DOI
Clement, A. E.; Liriano, S. Krull dimension and deviation in certain parafree groups. (English) Zbl 1220.20027 Commun. Algebra 38, No. 6, 2229-2239 (2010). MSC: 20F22 20F14 20E26 20F05 20C15 14L30 14Q15 PDFBibTeX XMLCite \textit{A. E. Clement} and \textit{S. Liriano}, Commun. Algebra 38, No. 6, 2229--2239 (2010; Zbl 1220.20027) Full Text: DOI arXiv
Drensky, Vesselin; Yu, Jie-Tai Degree estimate for commutators. (English) Zbl 1187.16024 J. Algebra 322, No. 7, 2321-2334 (2009). Reviewer: Plamen Koshlukov (Campinas) MSC: 16S10 16W20 16S36 16W22 13F20 14R10 PDFBibTeX XMLCite \textit{V. Drensky} and \textit{J.-T. Yu}, J. Algebra 322, No. 7, 2321--2334 (2009; Zbl 1187.16024) Full Text: DOI arXiv
Blatherwick, Vikki A. Centraliser dimension of free partially commutative nilpotent groups of class 2. (English) Zbl 1149.20029 Glasg. Math. J. 50, No. 2, 251-269 (2008). Reviewer: V. A. Roman’kov (Omsk) MSC: 20F18 20E05 20E10 14A22 05C25 20F05 20F36 PDFBibTeX XMLCite \textit{V. A. Blatherwick}, Glasg. Math. J. 50, No. 2, 251--269 (2008; Zbl 1149.20029) Full Text: DOI
Kharlampovich, Olga; Myasnikov, Alexei; Remeslennikov, Vladimir; Serbin, Denis Exponential extensions of groups. (English) Zbl 1135.20019 J. Group Theory 11, No. 1, 119-140 (2008). Reviewer: V. A. Roman’kov (Omsk) MSC: 20E22 20E26 20E05 20E08 20E07 20F67 20E06 14A22 PDFBibTeX XMLCite \textit{O. Kharlampovich} et al., J. Group Theory 11, No. 1, 119--140 (2008; Zbl 1135.20019) Full Text: DOI
Plotkin, Boris Some results and problems related to universal algebraic geometry. (English) Zbl 1154.08001 Int. J. Algebra Comput. 17, No. 5-6, 1133-1164 (2007). MSC: 08A99 08B99 14A99 PDFBibTeX XMLCite \textit{B. Plotkin}, Int. J. Algebra Comput. 17, No. 5--6, 1133--1164 (2007; Zbl 1154.08001) Full Text: DOI
Liriano, Sal Algebraic geometric invariants of parafree groups. (English) Zbl 1131.20022 Int. J. Algebra Comput. 17, No. 1, 155-169 (2007). Reviewer: V. A. Roman’kov (Omsk) MSC: 20F05 20F14 14L30 20C15 20G05 20F19 20E05 PDFBibTeX XMLCite \textit{S. Liriano}, Int. J. Algebra Comput. 17, No. 1, 155--169 (2007; Zbl 1131.20022) Full Text: DOI arXiv
Katsov, Y.; Lipyanski, R.; Plotkin, B. Automorphisms of categories of free modules, free semimodules, and free Lie modules. (English) Zbl 1121.16023 Commun. Algebra 35, No. 3, 931-952 (2007). Reviewer: Vesselin Drensky (Sofia) MSC: 16S10 16S38 16Y60 16D90 17B01 08A35 08C05 14A22 PDFBibTeX XMLCite \textit{Y. Katsov} et al., Commun. Algebra 35, No. 3, 931--952 (2007; Zbl 1121.16023) Full Text: DOI arXiv
Cantat, Serge; Lamy, Stéphane Groups of polynomial automorphisms of the plane. (Groupes d’automorphismes polynomiaux du plan.) (French) Zbl 1115.14055 Geom. Dedicata 123, 201-221 (2006). Reviewer: Jérémy Blanc (Bernex) MSC: 14R10 22E40 PDFBibTeX XMLCite \textit{S. Cantat} and \textit{S. Lamy}, Geom. Dedicata 123, 201--221 (2006; Zbl 1115.14055) Full Text: DOI
Kharlampovich, Olga; Myasnikov, Alexei Implicit function theorem over free groups. (English) Zbl 1094.20016 J. Algebra 290, No. 1, 1-203 (2005). Reviewer: V. A. Roman’kov (Omsk) MSC: 20F10 20E05 14A22 03B25 03C60 PDFBibTeX XMLCite \textit{O. Kharlampovich} and \textit{A. Myasnikov}, J. Algebra 290, No. 1, 1--203 (2005; Zbl 1094.20016) Full Text: DOI arXiv
Kvaschuk, Alexei; Myasnikov, Alexei; Remeslennikov, Vladimir Algebraic geometry over groups. III: Elements of model theory. (English) Zbl 1078.20025 J. Algebra 288, No. 1, 78-98 (2005). Reviewer: V. A. Roman’kov (Omsk) MSC: 20E10 14A22 03C60 20A15 20E05 20E34 20F10 20F65 20F05 PDFBibTeX XMLCite \textit{A. Kvaschuk} et al., J. Algebra 288, No. 1, 78--98 (2005; Zbl 1078.20025) Full Text: DOI
Mashevitzky, G.; Plotkin, B.; Plotkin, E. Automorphisms of categories of free algebras of varieties. (English) Zbl 0996.08008 Electron. Res. Announc. Am. Math. Soc. 2002, 1-10 (2002). MSC: 08C05 08B20 14A22 14A99 08A35 PDFBibTeX XMLCite \textit{G. Mashevitzky} et al., Electron. Res. Announc. Am. Math. Soc. 8, 1--10 (2002; Zbl 0996.08008) Full Text: DOI EuDML
Myasnikov, Alexei; Remeslennikov, Vladimir Algebraic geometry over groups. II: Logical foundations. (English) Zbl 0970.20017 J. Algebra 234, No. 1, 225-276 (2000). Reviewer: V.A.Roman’kov (Omsk) MSC: 20E34 20E05 14A22 20F10 08B05 08C15 08A45 20E06 20F05 20J15 20F65 PDFBibTeX XMLCite \textit{A. Myasnikov} and \textit{V. Remeslennikov}, J. Algebra 234, No. 1, 225--276 (2000; Zbl 0970.20017) Full Text: DOI Link
Berzins, A.; Plotkin, B.; Plotkin, E. Algebraic geometry in varieties of algebras with the given algebra of constants. (English) Zbl 0965.08010 J. Math. Sci., New York 102, No. 3, 4039-4070 (2000). Reviewer: Boris Vernikov (Ekaterinburg) MSC: 08B99 14A22 PDFBibTeX XMLCite \textit{A. Berzins} et al., J. Math. Sci., New York 102, No. 3, 4039--4070 (2000; Zbl 0965.08010) Full Text: DOI
Baumslag, Gilbert; Myasnikov, Alexei; Remeslennikov, Vladimir Algebraic geometry over groups. I: Algebraic sets and ideal theory. (English) Zbl 0938.20020 J. Algebra 219, No. 1, 16-79 (1999). Reviewer: V.A.Roman’kov (Omsk) MSC: 20E05 20E34 14A22 20E06 20E07 20F65 20J15 PDFBibTeX XMLCite \textit{G. Baumslag} et al., J. Algebra 219, No. 1, 16--79 (1999; Zbl 0938.20020) Full Text: DOI
Ignatenko, V. F. Invariants of finite and infinite groups generated by reflections. (English) Zbl 0845.20035 J. Math. Sci., New York 78, No. 3, 334-361 (1996). MSC: 20H15 51F15 20F55 14L35 PDFBibTeX XMLCite \textit{V. F. Ignatenko}, J. Math. Sci., New York 78, No. 3, 334--361 (1996; Zbl 0845.20035) Full Text: DOI