Mikhalev, Alexander A.; Mustafa, Manat; Umirbaev, Ualbai Representations via differential algebras and equationally Noetherian algebras. (English) Zbl 07725314 J. Algebra 633, 814-830 (2023). Reviewer: Plamen Koshlukov (Campinas) MSC: 12H05 17B63 17B66 17D25 16P40 17A50 PDFBibTeX XMLCite \textit{A. A. Mikhalev} et al., J. Algebra 633, 814--830 (2023; Zbl 07725314) Full Text: DOI arXiv
Artamonov, V. A.; Klimakov, A. V.; Mikhalev, A. A.; Mikhalev, A. V. Primitive and almost primitive elements of Schreier varieties. (English. Russian original) Zbl 1485.17017 J. Math. Sci., New York 237, No. 2, 157-179 (2019); translation from Fundam. Prikl. Mat. 21, No. 2, 3-35 (2016). Reviewer: Mark S. Burgin (Los Angeles) MSC: 17A50 17B35 16D90 08B20 PDFBibTeX XMLCite \textit{V. A. Artamonov} et al., J. Math. Sci., New York 237, No. 2, 157--179 (2019; Zbl 1485.17017); translation from Fundam. Prikl. Mat. 21, No. 2, 3--35 (2016) Full Text: DOI
Mikhalev, Alexander A.; Shestakov, Ivan P. PBW-pairs of varieties of linear algebras. (English) Zbl 1300.17006 Commun. Algebra 42, No. 2, 667-687 (2014). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 17A50 20N05 PDFBibTeX XMLCite \textit{A. A. Mikhalev} and \textit{I. P. Shestakov}, Commun. Algebra 42, No. 2, 667--687 (2014; Zbl 1300.17006) Full Text: DOI
Klimakov, A. V.; Mikhalev, A. A. Almost primitive elements of free nonassociative algebras of small ranks. (English. Russian original) Zbl 1317.17005 J. Math. Sci., New York 185, No. 3, 430-439 (2012); translation from Fundam. Prikl. Mat. 17, No. 1, 127-141 (2012). MSC: 17A50 PDFBibTeX XMLCite \textit{A. V. Klimakov} and \textit{A. A. Mikhalev}, J. Math. Sci., New York 185, No. 3, 430--439 (2012; Zbl 1317.17005); translation from Fundam. Prikl. Mat. 17, No. 1, 127--141 (2012) Full Text: DOI
Mikhalev, A. A.; Mikhalev, A. V.; Chepovskiĭ, A. A. Primitive elements of free commutative and anticommutative nonassociative algebras. (Russian. English summary) Zbl 1249.17013 Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 10, No. 4, 105-124 (2010). MSC: 17A50 17A36 PDFBibTeX XMLCite \textit{A. A. Mikhalev} et al., Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 10, No. 4, 105--124 (2010; Zbl 1249.17013)
Mikhalev, A. A.; Mikhalev, A. V.; Chepovskiĭ, A. A.; Champagnier, K. Primitive elements of free nonassociative algebras. (English. Russian original) Zbl 1215.17007 J. Math. Sci., New York 156, No. 2, 320-335 (2009); translation from Fundam. Prikl. Mat. 13, No. 5, 171-192 (2007). Reviewer: Victor Petrogradsky (Ulyanovsk) MSC: 17A50 17-04 17A36 17-08 PDFBibTeX XMLCite \textit{A. A. Mikhalev} et al., J. Math. Sci., New York 156, No. 2, 320--335 (2009; Zbl 1215.17007); translation from Fundam. Prikl. Mat. 13, No. 5, 171--192 (2007) Full Text: DOI
Mikhalev, Alexander A.; Shpilrain, Vladimir; Yu, Jie-Tai Combinatorial methods. Free groups, polynomials, and free algebras. (English) Zbl 1039.16024 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 19. New York, NY: Springer (ISBN 0-387-40562-3/hbk). xii, 315 p. (2004). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 16R10 16S36 17A32 20E05 16-02 17-02 20E36 20-02 17B01 13F20 PDFBibTeX XMLCite \textit{A. A. Mikhalev} et al., Combinatorial methods. Free groups, polynomials, and free algebras. New York, NY: Springer (2004; Zbl 1039.16024)
Artamonov, Vyacheslav A.; Mikhalev, Alexander A.; Mikhalev, Alexander V. Combinatorial properties of free algebras of Schreier varieties. (English) Zbl 1107.17300 Giambruno, Antonio (ed.) et al., Polynomial identities and combinatorial methods, Pantelleria, Italy. New York, NY: Marcel Dekker (ISBN 0-8247-4051-3/pbk). Lect. Notes Pure Appl. Math. 235, 47-99 (2003). Reviewer: Vesselin Drensky (Sofia) MSC: 17-02 16R10 17A36 17A50 17B01 17B40 17B75 PDFBibTeX XMLCite \textit{V. A. Artamonov} et al., Lect. Notes Pure Appl. Math. 235, 47--99 (2003; Zbl 1107.17300)
Mikhalev, Alexander A.; Yu, Jie-Tai Stable equivalence problems for free algebras with the Nielsen-Schreier property. (English) Zbl 1023.17002 Int. J. Algebra Comput. 11, No. 6, 779-786 (2001). Reviewer: Boris Vernikov (Ekaterinburg) MSC: 17B01 17A50 17B75 17B70 PDFBibTeX XMLCite \textit{A. A. Mikhalev} and \textit{J.-T. Yu}, Int. J. Algebra Comput. 11, No. 6, 779--786 (2001; Zbl 1023.17002) Full Text: DOI
Mikhalev, Alexander A.; Umirbaev, Ualbai; Yu, Jie-Tai Automorphic orbits in free non-associative algebras. (English) Zbl 1021.17003 J. Algebra 243, No. 1, 198-223 (2001). Reviewer: Mikhail Volkov (Ekaterinburg) MSC: 17A50 17A36 17D99 PDFBibTeX XMLCite \textit{A. A. Mikhalev} et al., J. Algebra 243, No. 1, 198--223 (2001; Zbl 1021.17003) Full Text: DOI
Abdykhalykov, A. T.; Mikhalev, A. A.; Umirbaev, U. U. Automorphisms of two-generated free Leibniz algebras. (English) Zbl 0978.17001 Commun. Algebra 29, No. 7, 2953-2960 (2001). Reviewer: Revaz Kurdiani (Tbilisi) MSC: 17A32 17A36 17A50 PDFBibTeX XMLCite \textit{A. T. Abdykhalykov} et al., Commun. Algebra 29, No. 7, 2953--2960 (2001; Zbl 0978.17001) Full Text: DOI
Mikhalev, Alexander A.; Shpilrain, Vladimir; Yu, Jie-Tai Combinatorial problems about free groups and algebras. (English) Zbl 1064.20025 Fong, Yuen (ed.) et al., Lie algebras, rings and related topics. Papers of the 2nd Tainan-Moscow international algebra workshop ’97, Tainan, Taiwan, January 11–17, 1997. Hong Kong: Springer (ISBN 962-430-110-7/pbk). 80-107 (2000). MSC: 20E05 16S36 20E36 16W20 17B01 17A50 14R10 16R10 16S10 PDFBibTeX XMLCite \textit{A. A. Mikhalev} et al., in: Lie algebras, rings and related topics. Papers of the 2nd Tainan-Moscow international algebra workshop '97, Tainan, Taiwan, January 11--17, 1997. Hong Kong: Springer. 80--107 (2000; Zbl 1064.20025) Full Text: arXiv
Mikhalev, A. A. Primitive elements and automorphisms of free algebras of Schreier varieties. (English) Zbl 1021.17002 J. Math. Sci., New York 102, No. 6, 4627-4639 (2000). Reviewer: Mikhail Volkov (Ekaterinburg) MSC: 17A50 17A36 17B01 17D99 17B40 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, J. Math. Sci., New York 102, No. 6, 4627--4639 (2000; Zbl 1021.17002) Full Text: DOI
Mikhalev, Alexander A.; Yu, Jie-Tai Automorphic orbits of elements of free algebras with the Nielsen-Schreier property. (English) Zbl 0982.17002 Chan, Kai Yuen (ed.) et al., Combinatorial and computational algebra. International conference on combinatorial and computational algebra, May 24-29, 1999, Hong Kong, China. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 264, 95-110 (2000). Reviewer: L.A.Bokut’ (Novosibirsk) MSC: 17A50 17B01 08B20 17B75 PDFBibTeX XMLCite \textit{A. A. Mikhalev} and \textit{J.-T. Yu}, Contemp. Math. 264, 95--110 (2000; Zbl 0982.17002)
Mikhalev, Alexander A.; Yu, Jietai Primitive, almost primitive, test, and \(\Delta\)-primitive elements of free algebras with the Nielsen-Schreier property. (English) Zbl 0956.17001 J. Algebra 228, No. 2, 603-623 (2000). Reviewer: V.A.Artamonov (Moskva) MSC: 17A50 17B01 PDFBibTeX XMLCite \textit{A. A. Mikhalev} and \textit{J. Yu}, J. Algebra 228, No. 2, 603--623 (2000; Zbl 0956.17001) Full Text: DOI
Mikhalev, Alexander A.; Shpilrain, Vladimir; Yu, Jie-Tai On endomorphisms of free algebras. (English) Zbl 0946.17001 Algebra Colloq. 6, No. 3, 241-248 (1999). Reviewer: P.M.Cohn (London) MSC: 17A50 PDFBibTeX XMLCite \textit{A. A. Mikhalev} et al., Algebra Colloq. 6, No. 3, 241--248 (1999; Zbl 0946.17001)
Mikhalev, Alexander A.; Yu, Jie-Tai Test elements, retracts and automorphic orbits of free algebras. (English) Zbl 0923.17006 Int. J. Algebra Comput. 8, No. 3, 295-310 (1998). Reviewer: A.A.Mikhalev (Moskva) MSC: 17B01 17A50 17A36 17A70 17B40 17B70 PDFBibTeX XML Full Text: DOI
Mikhalev, Alexander A.; Umirbaev, Ualbai U. Subalgebras of free Leibniz algebras. (English) Zbl 0892.17002 Commun. Algebra 26, No. 2, 435-446 (1998). Reviewer: B.Vernikov (Ekaterinburg) MSC: 17A30 17A50 PDFBibTeX XMLCite \textit{A. A. Mikhalev} and \textit{U. U. Umirbaev}, Commun. Algebra 26, No. 2, 435--446 (1998; Zbl 0892.17002) Full Text: DOI
Mikhalev, Alexander A.; Yu, Jie-Tai Test elements and retracts of free Lie algebras. (English) Zbl 0881.17003 Commun. Algebra 25, No. 10, 3283-3289 (1997). Reviewer: V.Drensky (Sofia) MSC: 17B01 17B40 17A70 17A50 17A36 PDFBibTeX XMLCite \textit{A. A. Mikhalev} and \textit{J.-T. Yu}, Commun. Algebra 25, No. 10, 3283--3289 (1997; Zbl 0881.17003) Full Text: DOI
Vasil’eva, E. A.; Mikhalëv, A. A. Free left-symmetric superalgebras. (Russian. English summary) Zbl 0903.17004 Fundam. Prikl. Mat. 2, No. 2, 611-613 (1996). Reviewer: V.Drensky (Sofia) MSC: 17A70 17A50 17B35 17B70 PDFBibTeX XMLCite \textit{E. A. Vasil'eva} and \textit{A. A. Mikhalëv}, Fundam. Prikl. Mat. 2, No. 2, 611--613 (1996; Zbl 0903.17004)
Mikhalev, A. A.; Zolotykh, A. A. Combinatorial aspects of Lie superalgebras. (English) Zbl 0871.17002 Boca Raton, FL: CRC Press. viii, 260 p. with Disc (1995). Reviewer: V.Drensky (Sofia) MSC: 17B01 17-02 17B35 17B40 17-08 17A70 68W30 68R15 PDFBibTeX XMLCite \textit{A. A. Mikhalev} and \textit{A. A. Zolotykh}, Combinatorial aspects of Lie superalgebras. Boca Raton, FL: CRC Press (1995; Zbl 0871.17002)
Zolotykh, A. A.; Mikhalev, A. A. The rank of an element of a free Lie \((p-)\)superalgebra. (English. Russian original) Zbl 0839.17002 Russ. Acad. Sci., Dokl., Math. 49, No. 1, 189-193 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 6, 690-693 (1994). Reviewer: P.M.Cohn (London) MSC: 17A70 17B01 PDFBibTeX XMLCite \textit{A. A. Zolotykh} and \textit{A. A. Mikhalev}, Russ. Acad. Sci., Dokl., Math. 49, No. 1, 690--693 (1994; Zbl 0839.17002); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 6, 690--693 (1994)
Mikhalev, Alexander A.; Zolotykh, Andrej A. Automorphisms and primitive elements of free Lie superalgebras. (English) Zbl 0815.17002 Commun. Algebra 22, No. 14, 5889-5901 (1994). Reviewer: H.F.Smith (Armidale) MSC: 17A70 17B01 PDFBibTeX XMLCite \textit{A. A. Mikhalev} and \textit{A. A. Zolotykh}, Commun. Algebra 22, No. 14, 5889--5901 (1994; Zbl 0815.17002) Full Text: DOI
Zolotykh, A. A.; Mikhalev, A. A. An endomorphism of a free Lie algebra that preserves the property of primitiveness of elements is an automorphism. (English. Russian original) Zbl 0828.17007 Russ. Math. Surv. 48, No. 6, 189-190 (1993); translation from Usp. Mat. Nauk 48, No. 6(294), 149-150 (1993). Reviewer: V.Drensky (Sofia) MSC: 17B01 17B40 17A70 PDFBibTeX XMLCite \textit{A. A. Zolotykh} and \textit{A. A. Mikhalev}, Russ. Math. Surv. 48, No. 6, 1 (1993; Zbl 0828.17007); translation from Usp. Mat. Nauk 48, No. 6(294), 149--150 (1993) Full Text: DOI
Mikhalëv, A. A. Images of inner derivations of free Lie algebras and superalgebras. (English. Russian original) Zbl 0817.17007 Mosc. Univ. Math. Bull. 48, No. 1, 34-36 (1993); translation from Vestn. Mosk. Univ., Ser. I 1993, No. 1, 35-38 (1993). Reviewer: V.Drensky (Sofia) MSC: 17B01 17B40 17B70 17A70 PDFBibTeX XMLCite \textit{A. A. Mikhalëv}, Mosc. Univ. Math. Bull. 48, No. 1, 35--38 (1993; Zbl 0817.17007); translation from Vestn. Mosk. Univ., Ser. I 1993, No. 1, 35--38 (1993)
Mikhalev, A. A. On fixed points of a free chromatic Lie superalgebra under the action of a finite group of linear automorphisms. (English. Russian original) Zbl 0792.17005 Russ. Math. Surv. 47, No. 4, 220-221 (1992); translation from Usp. Mat. Nauk 47, No. 4(286), 205-206 (1992). Reviewer: V.A.Artamonov (Moskva) MSC: 17A70 17B65 17B70 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, Russ. Math. Surv. 47, No. 4, 205--206 (1992; Zbl 0792.17005); translation from Usp. Mat. Nauk 47, No. 4(286), 205--206 (1992) Full Text: DOI
Mikhalev, A. A. Free Lie superrings. (Russian) Zbl 0816.17001 Lupanov, O. B. (ed.) et al., Algebra, geometry and discrete mathematics in nonlinear problems. Moskva: Izdatel’stvo Moskovskogo Universiteta. 107-111 (1991). Reviewer: H.F.Smith (Armidale) MSC: 17A70 17B01 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, in: Алгебра, геометрия и дискретная математика в нелинейных задачах. Moskva: Izdatel'stvo Moskovskogo Universiteta. 107--111 (1991; Zbl 0816.17001)
Mikhalev, A. A. Ado-Iwasawa theorem, graded Hopf algebras and residual finiteness of colored (\(p\)-) Lie superalgebras and their universal enveloping algebras. (Russian) Zbl 0751.17002 Vestn. Mosk. Univ., Ser. I 1991, No. 5, 72-74 (1991). Reviewer: Yu.A.Bakhturin (Moskva) MSC: 17A70 17B70 17B35 17B50 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, Vestn. Mosk. Univ., Ser. I 1991, No. 5, 72--74 (1991; Zbl 0751.17002)
Mikhalev, A. A. Free color Lie super-rings. (English. Russian original) Zbl 0744.17033 Sov. Math. 35, No. 10, 42-44 (1991); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1991, No. 10(353), 46-49 (1991). Reviewer: Yu.N.Mal’tsev (Barnaul) MSC: 17B70 17A70 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, Sov. Math. 35, No. 10, 42--44 (1991; Zbl 0744.17033); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1991, No. 10(353), 46--49 (1991)
Mikhalev, A. A. Ado-Iwasawa theorem, graded Hopf algebras, and properness of color Lie (\(p\)-) superalgebras and their universal enveloping algebras. (English. Russian original) Zbl 0784.17006 Mosc. Univ. Math. Bull. 46, No. 5, 51-53 (1991); translation from Vestn. Mosk. Univ., Ser. I 1991, No. 5, 72-74 (1991). MSC: 17A70 17B70 17B35 17B50 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, Mosc. Univ. Math. Bull. 46, No. 5, 51--53 (1991; Zbl 0784.17006); translation from Vestn. Mosk. Univ., Ser. I 1991, No. 5, 72--74 (1991)
Mikhalev, A. A. A composition lemma and the equality problem for color Lie superalgebras. (English. Russian original) Zbl 0705.17004 Mosc. Univ. Math. Bull. 44, No. 5, 87-90 (1989); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 5, 88-91 (1989). Reviewer: E.Khukhro MSC: 17A70 17B99 03D40 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, Mosc. Univ. Math. Bull. 44, No. 5, 87--90 (1989; Zbl 0705.17004); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 5, 88--91 (1989)
Mikhalev, A. A. Subalgebras of free Lie p-superalgebras. (English. Russian original) Zbl 0658.17020 Math. Notes 43, No. 2, 99-106 (1988); translation from Mat. Zametki 43, No. 2, 178-191 (1988). MSC: 17B70 17A70 17B05 17B50 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, Math. Notes 43, No. 2, 99--106 (1988; Zbl 0658.17020); translation from Mat. Zametki 43, No. 2, 178--191 (1988) Full Text: DOI
Mikhalev, A. A. Subalgebras of free Lie p-superalgebras. (Russian) Zbl 0646.17008 Mat. Zametki 43, No. 2, 178-191 (1988). Reviewer: Yu.A.Bakhturin MSC: 17B70 17B05 17A70 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, Mat. Zametki 43, No. 2, 178--191 (1988; Zbl 0646.17008)
Mikhalev, A. A. Subalgebras of free colored Lie superalgebras. (English) Zbl 0583.17003 Math. Notes 37, 356-360 (1985). MSC: 17A70 PDFBibTeX XMLCite \textit{A. A. Mikhalev}, Math. Notes 37, 356--360 (1985; Zbl 0583.17003) Full Text: DOI