Anatoly Ivanovich Maltsev (also: Malcev, Mal'cev; Russian: Анато́лий Ива́нович Ма́льцев; 27 November N.S./14 November O.S. 1909,

Moscow Governorate Moscow Governorate (russian: Московская губерния; pre-reform Russian: ), or the Government of Moscow, was an administrative division (a '' guberniya'') of the Tsardom of Russia, the Russian Empire, and the Russian SFSR, which ...

– 7 June 1967,

Novosibirsk Novosibirsk (, also ; rus, Новосиби́рск, p=nəvəsʲɪˈbʲirsk, a=ru-Новосибирск.ogg) is the largest city and administrative centre of Novosibirsk Oblast and Siberian Federal District in Russia. As of the Russian Census ...

) was born in

Misheronsky Misheronsky (russian: Мишеронский) is an urban locality (an urban-type settlement) in Shatursky District of Moscow Oblast, Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontine ...

, near Moscow, and died in

, USSR. He was a mathematician noted for his work on the decidability of various algebraic groups.

Malcev algebra In mathematics, a Malcev algebra (or Maltsev algebra or Moufang– Lie algebra) over a field is a nonassociative algebra that is antisymmetric, so that :xy = -yx and satisfies the Malcev identity :(xy)(xz) = ((xy)z)x + ((yz)x)x + ((zx)x)y. Th ...

s (generalisations of

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

s), as well as

Malcev Lie algebra In mathematics, a Malcev Lie algebra, or Mal'tsev Lie algebra, is a generalization of a rational nilpotent Lie algebra, and Malcev groups are similar. Both were introduced by , based on the work of . Definition According to a Malcev Lie algebra ...

s are named after him.

Biography

At school, Maltsev demonstrated an aptitude for mathematics, and when he left school in 1927, he went to Moscow State University to study

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 Ivanovo ( rus, Иваново, p=ɪˈvanəvə) is a types of inhabited localities in Russia, city in Russia. It is the administrative center and largest city of Ivanovo Oblast, located northeast of Moscow and approximately from Yaroslavl, Vlad ...

, 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 In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...

. 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 Ring may refer to: * Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry * To make a sound with a bell, and the sound made by a bell :(hence) to initiate a telephone connection Arts, entertainment and media Film and ...

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 Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part o ...

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 Ivanovo ( rus, Иваново, p=ɪˈvanəvə) is a city in Russia. It is the administrative center and largest city of Ivanovo Oblast, located northeast of Moscow and approximately from Yaroslavl, Vladimir and Kostroma. Ivanovo has a populat ...

Institute where he continued to work on group theory and linear groups in particular. He also studied

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

s and topological algebras. He generalized the

Lie group–Lie algebra correspondence In mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for such a relationship. Lie groups that are Isomorphism, isomorphic to each other have Lie algebras ...

; his generalization is now known as the Mal'cev correspondence. 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 ''Algebra i Logika'' (English: ''Algebra and Logic'') is a peer-reviewed Russian mathematical journal founded in 1962 by Anatoly Ivanovich Malcev, published by the Siberian Fund for Algebra and Logic at Novosibirsk State University. An English ...

''. Maltsev also founded the "Algebra and Logic Seminar" attended by his students Igor Lavrov,

Larisa Maksimova Larisa Lvovna Maksimova (russian: Лариса Львовна Максимова; born 1943) is a Russian mathematical logician known for her research in non-classical logic. Education and career Maksimova was born on November 5, 1943, in Kochenyo ...

, Dmitry Smirnov, Mikhail Taitslin, and A. Vinogradov, as well as by

Yuri Ershov Yury Leonidovich Yershov (, born 1 May 194 is a Soviet and Russian mathematician. Yury Yershov was born in 1940 in Novosibirsk. In 1958 he entered the Tomsk State University and in 1963 graduated from the Mathematical Department of the Novosi ...

and others. This seminar, in essence, started a new and extremely fruitful school in

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 group Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked ...

s, 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 ''

''.

Selected publications

*''Algebraic Systems'' by A.I. Mal'cev, Springer-Verlag, 1973, *''The metamathematics of algebraic systems, collected papers:1936-1967'' by A.I. Malcev, Amsterdam, North-Holland Pub. Co., 1971, (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 *''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)

References

External links

* * {{DEFAULTSORT:Maltsev, Anatoly 1909 births 1967 deaths Lenin Prize winners Full Members of the USSR Academy of Sciences Moscow State University alumni Soviet mathematicians Stalin Prize winners Model theorists Novosibirsk State University academic personnel Burials at Yuzhnoye Cemetery (Novosibirsk)

Biography

Selected publications

See also

References

External links