Anatoly Ivanovich Malzew

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Anatoly Maltsev ( Russian Анатолий Иванович Мальцев , scientific. Transliteration Anatoly Ivanovich Mal'cev ; in English transcribed Anatoly Ivanovich Malcev; born 14 jul. / 27. November  1909 greg. In Mischeronski at Shatura , † 7. July 1967 in Novosibirsk ) was a Russian mathematician and logician.


He studied mathematics in Moscow from 1927 to 1931 . At the Steklow Institute he was an aspirant from 1934 to 1937, a doctoral student from 1939 to 1941 and a research assistant from 1942 to 1960. In 1941 he received his doctorate in physical-mathematical sciences. In 1958, the Academy of Sciences of the USSR accepted him as a member.

From 1932 to 1960 he also 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 Algebra Section at the Mathematical Institute of the Siberian Department of the AdW of the USSR and the Chair of Algebra and Mathematical Logic at the university there.

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).

Juri Leonidowitsch Jerschow is one of his doctoral students . His last aspirant was Larissa Lvovna Maximova .

The Russian Academy of Sciences has been awarding the Malcev Prize for outstanding mathematical achievements since 1992.


His main areas of work were algebra and model theory . Numerous fundamental results on the theory of groups and rings, on the theory of Lie groups and on topological algebra can be traced back to him. In particular, he made significant contributions to the solution of Hilbert's 5th problem , the foundation of Lie's theory of continuous transformation groups, if possible without prerequisites for differentiability.

His work on the theory of algebraic systems concerns the border area between algebra and logic, which has been known as model theory since around 1960 and was one of its founder, Malzew. From him u. a. the first use of the compactness theorem of mathematical logic in the proof of content-rich theorems of group theory in 1941.

Numerous studies by him and the Novosibirsk School of Model Theory, which he had built, dealt with questions of the axiomatizability and decidability of concrete algebraic structural classes. He was the founder of a theory of constructive algebras , in which a combination of ideas and methods of recursion theory with those of universal algebra is established.

Malzew gave a general formulation of the compactness theorem as early as 1936. He dealt in depth with the recursion theory and developed a theory of numbered sets and algebras in particular .


  • Studies from the field of mathematical logic , in: Mat. Sb. 1 (1936), pp. 323–336.
  • Osnowy linejnoj algebry , Moscow / Leningrad, Ogis, 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, English: 1973.
  • The mathematics of algebaric systems , summary of his work on logic and metamathematics from 1936 to 1967, 1971.
  • Algorithms and Recursive Functions , Berlin, Akademie-Verlag, 1974.

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