Anatoly Ivanovich Malcev

Anatoly Ivanovich Maltsev (Malcev) (Russian: Анато́лий Ива́нович Ма́льцев) was born 27 November (14 November, old style) 1909 in Misheronsky, near Moscow, and died 7 June 1967 in Novosibirsk, USSR. He was a mathematician noted for his work on the decidability of various algebraic groups. Maltsev algebras (generalisations of Lie algebras) are named after him. November 27 is the 331st day (332nd on leap years) of the year. ... 1909 was a common year starting on Friday (see link for calendar). ... Moscow (Russian: Москва́, Moskva, IPA: listen â–¶(?)) is the capital of Russia, located on the river Moskva. ... June 7 is the 158th day of the year in the Gregorian calendar (159th in leap years), with 207 days remaining. ... 1967 (MCMLXVII) was a common year starting on Sunday of the Gregorian calendar. ... Novosibirsk (Russian Новосиби́рск, pop. ... A mathematician is a person whose area of study and research is mathematics. ... The word decidable has formal meaning in computability theory, the theory of formal languages, and mathematical logic. ... In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. ... In mathematics, a Lie algebra is an algebraic structure whose main use lies in studying geometric objects such as Lie groups and differentiable manifolds. ...

At school, Maltsev demonstrated an aptitude for mathematics, and when he left school in 1927, he went to Moscow State University to study 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. Moscow State University campus M.V. Lomonosov Moscow State University (Russian: Московский Государственный Университет имени М.В.Ломоносова, often abbreviated МГУ, MSU, MGU) is the largest and oldest university in Russia, founded in 1755. ... Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ...

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. Kolmogorov soon invited him to join his graduate programme at Moscow University, and, maintaining his post at Ivanovo, Maltsev effectively became Kolmogorov's student. Andrey Kolmogorov Andrey Nikolaevich Kolmogorov (Андре́й Никола́евич Колмого́ров) (kahl-mah-GAW-raff) (April 25, 1903 in Tambov - October 20, 1987 in Moscow) was a Russian mathematician who made major advances in the fields of probability theory and topology. ... Logic (from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy amongst philosophers (see below). ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems. ...

In 1937, Maltsev published a paper on the embeddability of a ring 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. In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have similar (but not identical) properties to those familiar from the integers. ... In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers. ... In mathematics, a semigroup is a set with an associative binary operation on it. ... In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. ...

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. Russian Academy of Sciences (Росси́йская Акаде́мия Нау́к) is the national academy of Russia. ...

In 1944, Maltsev became a professor at the Ivanovo Pedagogical Institute where he continued to work on group theory and linear groups in particular. He also studied Lie groups and topological algebras. Group theory is that branch of mathematics concerned with the study of groups. ... In mathematics, the general linear group of degree n over a field F (such as R or C), written as GL(n, F), is the group of n×n invertible matrices with entries from F, with the group operation that of ordinary matrix multiplication. ... In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ... In mathematics, an algebra over a field K, or a K-algebra, is a vector space A over K equipped with a compatible notion of multiplication of elements of A. A straightforward generalisation allows K to be any commutative ring. ...

In 1958, Maltsev became an Academician of the Soviet Academy of Sciences. Russian Academy of Sciences (Росси́йская Акаде́мия Нау́к) is the national academy of Russia. ...

In 1960, Maltsev 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 essense, started a new and extremely fruitful school in model theory and decidability of elementary theories. Yuri L. Ershov is a russian mathematician. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems. ...

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 groups, 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. In mathematics, a finite group is a group which has finitely many elements. ... In group theory, a nilpotent group is a group having a special property that makes it almost abelian, through repeated application of the commutator operation, [x,y] = x-1y-1xy. ... In the history of mathematics, the origins of group theory lie in the search for a proof of the general unsolvability of quintic and higher equations, finally realized by Galois theory. ...

Maltsev received many honours, including the Lenin Prize in 1964. Lenin Prize (Russian: Ле́нинская пре́мия) was one of the highest awards in the Soviet Union. ...

In 1962 he founded the mathematical journal Algebra i Logika.

Bibliography

• Algebraic Systems by A.I. Malcev, Springer-Verlag, 1973, ISBN 0387057927
• The metamathematics of algebraic systems, collected papers:1936-1967 by A.I. Malcev, Amsterdam, North-Holland Pub. Co., 1971, ISBN 0720422663
• 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

External link

• MacTutor biography