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

Moscow Governorate The Moscow Governorate was a province ('' guberniya'') of the Tsardom of Russia, and the Russian Empire. It was bordered by Tver Governorate to the north, Vladimir Governorate to the northeast, Ryazan Governorate to the southeast, Tula Gove ...

– 7 June 1967,

Novosibirsk Novosibirsk is the largest city and administrative centre of Novosibirsk Oblast and the Siberian Federal District in Russia. As of the 2021 Russian census, 2021 census, it had a population of 1,633,595, making it the most populous city in Siber ...

) was born in Misheronsky, near

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

, and died in

USSR The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

. 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, mathematical structure, structure, space, Mathematica ...

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 that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Man ...

s. Malcev algebras (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 ident ...

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 Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

to study

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. 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 (, ) is a types of inhabited localities in Russia, city in Russia and the administrative center and largest city of Ivanovo Oblast, located northeast of Moscow and approximately from Yaroslavl, Vladimir, Russia, Vladimir and Kostroma. ...

, 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 Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

and

model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

. 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 (mathematics), group that is a subgroup. When some object X is said to be embedded in another object Y ...

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 (just notation, not necessarily th ...

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 In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

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 ...

s in particular. He also studied

Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Eucli ...

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 algebra ...

; 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''. 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 In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving tra ...

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, it has a central series of finite length or its lower central series terminates with . I ...

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 terminat ...

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 The Lenin Prize (, ) was one of the most prestigious awards of the Soviet Union for accomplishments relating to science, literature, arts, architecture, and technology. It was originally created on June 23, 1925, and awarded until 1934. During ...

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 Recipients of the Lenin Prize Full Members of the USSR Academy of Sciences Moscow State University alumni Soviet mathematicians Recipients of the Stalin Prize Model theorists Academic staff of Novosibirsk State University Burials at Yuzhnoye Cemetery (Novosibirsk) Russian scientists

Biography

Selected publications

See also

References

External links