**Anatoly Malcev** was a Russian mathematician noted for his work on the decidability of various algebraic structures.

- Malcev graduated from school in 1927 and, in the same year, he went to Moscow State University to study mathematics.
- The town, on both banks of the Uvod River, had been known as Ivanovo-Voznesensk but was renamed Ivanovo in 1932, the year Malcev started to work there.
- When Malcev began teaching in Ivanovo he had only a first degree but Ivanovo had a good rail link with Moscow and he was able to make frequent trips there to discuss his research with Kolmogorov.
- Malcev's first publications were on logic and model theory and resulted from work he had begun entirely on his own.
- Kolmogorov invited Malcev to join his graduate programme at Moscow University, and he held a studentship there for a year although he continued his teaching post at the Ivanovo Pedagogical Institute during the year.
- Malcev always considered himself to have been Kolmogorov's student and certainly during the year he held the studentship at Moscow University, Malcev was directed by Kolmogorov to certain algebra problems.
- In 1937 Malcev published a paper on the embeddability of a ring in a field, answering a question posed by Kolmogorov.
- Malcev answered this question by constructing a ring whose multiplicative semigroup was not embeddable in a group.
- This led, two years later, to another fundamental paper of Malcev where he gave necessary and sufficient conditions for a semigroup to be embeddable in a group.
- In 1937 Malcev wrote a dissertation on Torsion free abelian groups of finite rank then, between 1939 and 1941, he studied for his doctorate (which in Russia is similar to the habilitation) at the Steklov Institute of the USSR Academy of Sciences.
- During this period in which he undertook doctoral research Malcev continued as a lecturer at the Ivanovo Pedagogical Institute.
- Malcev became a professor at Ivanovo Pedagogical Institute in 1944.
- Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic.
- Malcev also created a synthesis of the theory of algebras and of algorithms called constructive algebras.
- In 1960, Malcev was appointed to a chair in mathematics at the Mathematics Institute at Novosibirsk and to be chairman of the Algebra and Logic Department at Novosibirsk State University.
- In 1962 Malcev founded the specialised journal Algebra i Logika and from that time he was editor of this journal.
- During the early 1960s Malcev worked on problems of decidability of elementary theories of various algebraic structures.
- In 1948 Malcev wrote the undergraduate text Foundation of linear algebra which appeared in English translation in 1962.
- Just before his death Malcev had delivered his final lecture at this Novosibirsk Topology Conference.
- It was on algebras, now called Malcev algebras, which are natural generalisations of Lie algebras.
- Malcev had introduced these algebras in 1955 and in this lecture he gave a survey of his work on this topic over the twelve preceding years.
- Malcev received many honours, and world-wide recognition for his innovative work.

Born 27 November 1909, Misheronsky (near Moscow), Russia. Died 7 July 1967, Novosibirsk, USSR.

View full biography at MacTutor

Group Theory, Origin Russia

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive