Viktor Vladimirovich Wagner, also Vagner () (4 November 1908 – 15 August 1981) was a Russian
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 ...
, best known for his work in
differential geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...
and on
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 ...
s.
Wagner was born in
Saratov
Saratov ( , ; , ) is the largest types of inhabited localities in Russia, city and administrative center of Saratov Oblast, Russia, and a major port on the Volga River. Saratov had a population of 901,361, making it the List of cities and tow ...
and studied at
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 ...
, where
Veniamin Kagan was his advisor. He became the first geometry chair at
Saratov State University
Saratov Chernyshevsky State University (, СГУ, transcribed as SGU) is a higher education and research institution in Russia. In 2023 it was ranked #1,156 in the world by ''US News & World Report''.
Named for Nikolay Chernyshevsky, the univer ...
. He received the
Lobachevsky Medal in 1937.
Wagner was also awarded "the
Order of Lenin
The Order of Lenin (, ) was an award named after Vladimir Lenin, the leader of the October Revolution. It was established by the Central Executive Committee on 6 April 1930. The order was the highest civilian decoration bestowed by the Soviet ...
, the
Order of the Red Banner
The Order of the Red Banner () was the first Soviet military decoration. The Order was established on 16 September 1918, during the Russian Civil War by decree of the All-Russian Central Executive Committee. It was the highest award of S ...
, and the title of Honoured Scientist RSFSR. Moreover, he was also accorded that rarest of privileges in the USSR: permission to travel abroad."
Wagner is credited with noting that the collection of
partial transformations on a set ''X'' forms a semigroup
which is a subsemigroup of the semigroup
of
binary relation
In mathematics, a binary relation associates some elements of one Set (mathematics), set called the ''domain'' with some elements of another set called the ''codomain''. Precisely, a binary relation over sets X and Y is a set of ordered pairs ...
s on the same set ''X'', where the semigroup operation is
composition of relations
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation from two given binary relations ''R'' and ''S''. In the calculus of relations, the composition of relations is called relative multiplica ...
. "This simple unifying observation, which is nevertheless an important psychological hurdle, is attributed by Schein (1986) to V.V. Wagner."
[Peter M. Higgins (1992) ''Techniques of Semigroup Theory'', page 5, ]Oxford University Press
Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...
See also
*
Inverse semigroup In group (mathematics), group theory, an inverse semigroup (occasionally called an inversion semigroup) ''S'' is a semigroup in which every element ''x'' in ''S'' has a unique ''inverse'' ''y'' in ''S'' in the sense that and , i.e. a regular semigr ...
*
Heap
References
*
External links
*
*
Wagner's Biography– in Russian
{{DEFAULTSORT:Wagner, Viktor Vladimirovich
Soviet mathematicians
Academic staff of Saratov State University
Moscow State University alumni
Differential geometers
Algebraists
20th-century Russian mathematicians
1908 births
1981 deaths