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Anatoly Ivanovich Malcev was born 27 November 1909 in Misheronsky, near Moscow, and died 7 July 1967 in Novosibirsk, USSR. He was a mathematician noted for his work on the decidability of various algebraic groups. Malcev algebras (generalisations of Lie algebras) are named after him.
At school, Malcev 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.
Whilst teaching at Ivanovo, Malcev made frequent trips to Moscow to discuss his research with Kolmogorov. Malcev'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 Ivanova, Malcev effectively became Kalmogorov's student.
In 1937, Malcev 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.
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, Malcev 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.
In 1960, Malcev 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".
During the early 1960s, Malcev 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 had a decidable theory.
Malcev received many honours, including the Lenin Prize in 1964.
External link
- MacTutor biography (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Malcev.html)
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