fbpx
Wikipedia

Anatoly Maltsev

December 15, 2023

Anatoly Ivanovich Maltsev (also: Malcev, Mal'cev; Russian: Анато́лий Ива́нович Ма́льцев; 27 November N.S./14 November O.S. 1909, Moscow Governorate – 7 June 1967, Novosibirsk) was born in Misheronsky, near Moscow, and died in Novosibirsk, USSR. He was a mathematician noted for his work on the decidability of various algebraic groups. Malcev algebras (generalisations of Lie algebras), as well as Malcev Lie algebras are named after him.

Biography edit

At school, Maltsev demonstrated an aptitude for mathematics, and when he left school in 1927, he went to Moscow State University to study Mathematics. While he was there, he started teaching in a secondary school in Moscow. After graduating in 1931, he continued his teaching career and in 1932 was appointed as an assistant at the Ivanovo Pedagogical Institute located in Ivanovo, near Moscow.

Whilst teaching at Ivanovo, Maltsev made frequent trips to Moscow to discuss his research with Kolmogorov. Maltsev's first publications were on logic and model theory. Kolmogorov soon invited him to join his graduate programme at Moscow State University, and, maintaining his post at Ivanovo, Maltsev effectively became Kolmogorov's student.

In 1937, Maltsev published a paper on the embedding of a ring in a field. Two years later, he published a second paper where he gave necessary and sufficient conditions for a semigroup to be embeddable in a group.

Between 1939 and 1941, he studied for his doctorate at the Steklov Institute of the USSR Academy of Sciences, with a dissertation on the Structure of isomorphic representable infinite algebras and groups.

In 1944, Maltsev became a professor at the Ivanovo Pedagogical Institute where he continued to work on group theory and linear groups in particular. He also studied Lie groups and topological algebras. He generalized the Lie group–Lie algebra correspondence;[1] his generalization is now known as the Mal'cev correspondence.[2][3]

Malcev[4] proved that there is a category isomorphism between the category of torsion-free radicable nilpotent groups of finite rank and the category of nilpotent finite-dimensional rational Lie algebras. One can view this isomorphism as being given by the Campbell–Baker–Hausdorff formula. This point of view is carried further by Lazard[5] and Stewart.[6]

In 1958, Maltsev became an Academician of the Soviet Academy of Sciences. In 1960, he was appointed to a chair in mathematics at the Mathematics Institute at Novosibirsk and chaired the Algebra and Logic Department of Novosibirsk State University. He founded the Siberian section of the Mathematics Institute of the Academy of Sciences, the Siberian Mathematical Society and the journal Algebra i Logika. Maltsev also founded the "Algebra and Logic Seminar" attended by his students Igor Lavrov, Larisa Maksimova, Dmitry Smirnov, Mikhail Taitslin, and A. Vinogradov, as well as by Yuri Ershov and others. This seminar, in essence, started a new and extremely fruitful school in model theory and decidability of elementary theories.

During the early 1960s, Maltsev worked on problems of decidability of elementary theories of various algebraic structures. He showed the undecidability of the elementary theory of finite groups, of free nilpotent groups, of free soluble groups and many others. He also proved that the class of locally free algebras has a decidable theory.

Maltsev received many honours, including the Stalin Prize in 1946 and Lenin Prize in 1964. In 1962 he founded the mathematical journal Algebra i Logika.

Selected publications edit

  • Algebraic Systems by A.I. Mal'cev, Springer-Verlag, 1973, ISBN 0-387-05792-7
  • The metamathematics of algebraic systems, collected papers:1936-1967 by A.I. Malcev, Amsterdam, North-Holland Pub. Co., 1971, ISBN 0-7204-2266-3 (xvii+494 p.; trans., ed. and provided with additional notes by Benjamin Franklin Wells, III)
  • Algorithms and recursive functions by A. I. Malcev, Groningen, Wolters-Noordhoff Pub. Co. 1970[7]
  • Foundations of linear algebra by A. I. Malcev, San Francisco, W.H. Freeman, 1963 (xi+304 p. illus.; trans. by Thomas Craig Brown; ed. by J. B. Roberts)

See also edit

References edit

  1. ^ Mostowski, Andrzej (1969). "Review: Model Correspondences by A.I. Mal'cev". Journal of Symbolic Logic. 34 (2): 299–300. doi:10.2307/2271119. JSTOR 2271119.
  2. ^ Stewart, Ian (1977). "Adjoint groups and the Mal'cev correspondence (a tale of four functors)". Fundamenta Mathematicae. 97 (2): 71–77. doi:10.4064/fm-97-2-71-77.
  3. ^ Videla, Carlos R. (1990). "On the Mal′cev correspondence". Proceedings of the American Mathematical Society. 109 (2): 493–502. doi:10.1090/S0002-9939-1990-1014647-9. JSTOR 2048013. MR 1014647.
  4. ^ Mal'cev, A. I. (1949). "Nilpotent torsion-free groups". Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya. 13: 201–212. ISSN 0373-2436. MR 0028843.
  5. ^ Lazard, Michel (1954). "Sur les groupes nilpotents et les anneaux de Lie". Annales Scientifiques de l'École Normale Supérieure. 71 (2): 101–190. doi:10.24033/asens.1021.
  6. ^ Warfield, Robert B. (1976). "The Malcev correspondence". Nilpotent Groups. Lecture Notes in Mathematics, Volume 513. Vol. 513. pp. 104–111. doi:10.1007/BFb0080164. ISBN 978-3-540-07683-4.
  7. ^ Algorithms and recursive functions in libraries (WorldCat catalog)

External links edit

December 15, 2023
anatoly, maltsev, anatoly, ivanovich, maltsev, also, malcev, russian, Анато, лий, Ива, нович, Ма, льцев, november, november, 1909, moscow, governorate, june, 1967, novosibirsk, born, misheronsky, near, moscow, died, novosibirsk, ussr, mathematician, noted, wor. Anatoly Ivanovich Maltsev also Malcev Mal cev Russian Anato lij Iva novich Ma lcev 27 November N S 14 November O S 1909 Moscow Governorate 7 June 1967 Novosibirsk was born in Misheronsky near Moscow and died in Novosibirsk USSR He was a mathematician noted for his work on the decidability of various algebraic groups Malcev algebras generalisations of Lie algebras as well as Malcev Lie algebras are named after him Contents 1 Biography 2 Selected publications 3 See also 4 References 5 External linksBiography editAt school Maltsev demonstrated an aptitude for mathematics and when he left school in 1927 he went to Moscow State University to study Mathematics While he was there he started teaching in a secondary school in Moscow After graduating in 1931 he continued his teaching career and in 1932 was appointed as an assistant at the Ivanovo Pedagogical Institute located in Ivanovo near Moscow Whilst teaching at Ivanovo Maltsev made frequent trips to Moscow to discuss his research with Kolmogorov Maltsev s first publications were on logic and model theory Kolmogorov soon invited him to join his graduate programme at Moscow State University and maintaining his post at Ivanovo Maltsev effectively became Kolmogorov s student In 1937 Maltsev published a paper on the embedding of a ring in a field Two years later he published a second paper where he gave necessary and sufficient conditions for a semigroup to be embeddable in a group Between 1939 and 1941 he studied for his doctorate at the Steklov Institute of the USSR Academy of Sciences with a dissertation on the Structure of isomorphic representable infinite algebras and groups In 1944 Maltsev became a professor at the Ivanovo Pedagogical Institute where he continued to work on group theory and linear groups in particular He also studied Lie groups and topological algebras He generalized the Lie group Lie algebra correspondence 1 his generalization is now known as the Mal cev correspondence 2 3 Malcev 4 proved that there is a category isomorphism between the category of torsion free radicable nilpotent groups of finite rank and the category of nilpotent finite dimensional rational Lie algebras One can view this isomorphism as being given by the Campbell Baker Hausdorff formula This point of view is carried further by Lazard 5 and Stewart 6 In 1958 Maltsev became an Academician of the Soviet Academy of Sciences In 1960 he was appointed to a chair in mathematics at the Mathematics Institute at Novosibirsk and chaired the Algebra and Logic Department of Novosibirsk State University He founded the Siberian section of the Mathematics Institute of the Academy of Sciences the Siberian Mathematical Society and the journal Algebra i Logika Maltsev also founded the Algebra and Logic Seminar attended by his students Igor Lavrov Larisa Maksimova Dmitry Smirnov Mikhail Taitslin and A Vinogradov as well as by Yuri Ershov and others This seminar in essence started a new and extremely fruitful school in model theory and decidability of elementary theories During the early 1960s Maltsev worked on problems of decidability of elementary theories of various algebraic structures He showed the undecidability of the elementary theory of finite groups of free nilpotent groups of free soluble groups and many others He also proved that the class of locally free algebras has a decidable theory Maltsev received many honours including the Stalin Prize in 1946 and Lenin Prize in 1964 In 1962 he founded the mathematical journal Algebra i Logika Selected publications editAlgebraic Systems by A I Mal cev Springer Verlag 1973 ISBN 0 387 05792 7 The metamathematics of algebraic systems collected papers 1936 1967 by A I Malcev Amsterdam North Holland Pub Co 1971 ISBN 0 7204 2266 3 xvii 494 p trans ed and provided with additional notes by Benjamin Franklin Wells III Algorithms and recursive functions by A I Malcev Groningen Wolters Noordhoff Pub Co 1970 7 Foundations of linear algebra by A I Malcev San Francisco W H Freeman 1963 xi 304 p illus trans by Thomas Craig Brown ed by J B Roberts See also editHahn Mal cev Neumann series Malcev algebra Mal cev s criterion Malcev Lie algebra Malcev admissible algebraReferences edit Mostowski Andrzej 1969 Review Model Correspondences by A I Mal cev Journal of Symbolic Logic 34 2 299 300 doi 10 2307 2271119 JSTOR 2271119 Stewart Ian 1977 Adjoint groups and the Mal cev correspondence a tale of four functors Fundamenta Mathematicae 97 2 71 77 doi 10 4064 fm 97 2 71 77 Videla Carlos R 1990 On the Mal cev correspondence Proceedings of the American Mathematical Society 109 2 493 502 doi 10 1090 S0002 9939 1990 1014647 9 JSTOR 2048013 MR 1014647 Mal cev A I 1949 Nilpotent torsion free groups Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya 13 201 212 ISSN 0373 2436 MR 0028843 Lazard Michel 1954 Sur les groupes nilpotents et les anneaux de Lie Annales Scientifiques de l Ecole Normale Superieure 71 2 101 190 doi 10 24033 asens 1021 Warfield Robert B 1976 The Malcev correspondence Nilpotent Groups Lecture Notes in Mathematics Volume 513 Vol 513 pp 104 111 doi 10 1007 BFb0080164 ISBN 978 3 540 07683 4 Algorithms and recursive functions in libraries WorldCat catalog External links editAnatolij Ivanovich Mal tsev at the Mathematics Genealogy Project O Connor John J Robertson Edmund F Anatoly Ivanovich Malcev MacTutor History of Mathematics Archive University of St Andrews Retrieved from https en wikipedia org w index php title Anatoly Maltsev amp oldid 1185590224, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.