Anatoly Maltsev
Anatoly Ivanovich Maltsev (Russian Анатолий Иванович Мальцев, scientific transliteration Anatoly Ivanovich Mal'cev; Anatoly Ivanovich Malcev transcribed in English, . * 14.jul / November 27 1909greg in Mischeronski at Schatura; . † July 7, 1967 in Novosibirsk ) was a Russian mathematician and logician.
Life
He studied from 1927 to 1931 Mathematics in Moscow. At the Steklov Institute, he was from 1934 to 1937 aspirant, 1939-1941 PhD student and research assistant from 1942 to 1960. In 1941 he earned his doctorate as a doctor of physico- mathematical sciences. 1958 took him to the Academy of Sciences of the USSR as a member.
From 1932 to 1960 he worked as an assistant, then as a lecturer and from 1943 as a professor of higher algebra at the Pedagogical Institute in Ivanovo. From 1960, he headed the section algebra at the Mathematical Institute of the Siberian Branch of the Academy of Sciences of the USSR and the Chair of Algebra and Mathematical Logic the local university.
In 1966 he gave a plenary lecture at the International Congress of Mathematicians in Moscow ( On some questions on the border of algebra and logic ).
His doctoral counts Yuri Leonidovich Ershov.
Work
His main areas of work were the algebra and model theory. Many fundamental results in the theory of groups and rings, the theory of Lie groups and topological algebra go back to him. In particular, he made major contributions to the solution of Hilbert's fifth problem, the grounds of Lie theory of continuous transformation groups as possible without differentiability.
His work on the theory of algebraic systems related to the border area of algebra and logic, which is known as model theory since about 1960 and was one of its founder Maltsev. From him comes, inter alia, the first use of the compactness theorem of mathematical logic in the proof of content-rich sets of group theory in 1941.
Numerous investigations of him and he built the Novosibirsk school of model theory had questions of axiomatization and decidability of specific algebraic structure classes for the subject. He was the founder of a theory of constructive algebras, in which a combination of ideas and methods of recursion theory is made with such universal algebra.
Maltsev was in 1936 a general formulation of the compactness theorem. It dealt in detail with the recursion and developed here in particular a theory of numbered sets and algebras.
Writings
- Research from the field of mathematical logic, in: Mat Sb 1 (1936 ), pp. 323-336
- Osnowy linejnoj algebry, Moscow / Leningrad, Ogi, 1948
- Foundations of Linear Algebra, WH Freeman & Company 1963
- Algorithms and recursive functions, Wolters- Noordhoff Publishing, Netherlands 1970
- Algoritmi i rekursiwenije funkzi, 1965, German: 1974
- Algebraischeskije sistemi, 1970, engl. 1973
- The mathematics of algebaric system, summary of his work of logic and meta-mathematics from 1936-1967, 1971
- Algorithms and Recursive Functions, Berlin, Akademie-Verlag, 1974