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 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 2021 Censu ...

) was born in Misheronsky, near

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 millio ...

, and died in

USSR The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nation ...

. He was a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History ...

noted for his work on the decidability of various

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Ma ...

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 operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identi ...

s), as well as Malcev Lie algebras 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 M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

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 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 popu ...

, near Moscow. Whilst teaching at Ivanovo, Maltsev made frequent trips to Moscow to discuss his research with

Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

. Maltsev's first publications were on

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premi ...

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 ...

. 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 In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X is said to be embedded in another object Y, the embedding is gi ...

of a ring in a field. Two years later, he published a second paper where he gave necessary and sufficient conditions for a

semigroup In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', ...

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 The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991, uniting the country's leading scientists, subordinated directly to the Council of Ministers of the Soviet Union (until 1946 ...

, 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 In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as ...

and

linear group In mathematics, a matrix group is a group ''G'' consisting of invertible matrices over a specified field ''K'', with the operation of matrix multiplication. A linear group is a group that is isomorphic to a matrix group (that is, admitting a fait ...

s 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 add ...

s and

topological algebra In mathematics, a topological algebra A is an algebra and at the same time a topological space, where the algebraic and the topological structures are coherent in a specified sense. Definition A topological algebra A over a topological field K is ...

s. He generalized the Lie group–Lie algebra correspondence; his generalization is now known as the Mal'cev correspondence. In 1958, Maltsev became an Academician of the

Soviet Academy of Sciences The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991, uniting the country's leading scientists, subordinated directly to the Council of Ministers of the Soviet Union (until 1946 ...

. 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

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 marke ...

s, of free

nilpotent group In mathematics, specifically group theory, a nilpotent group ''G'' is a group that has an upper central series that terminates with ''G''. Equivalently, its central series is of finite length or its lower central series terminates with . Intui ...

s, of free

soluble group In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates ...

s 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

*''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