Marc Krasner (1912 – 13 May 1985, in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

) was a Russian-born French mathematician, who worked on

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

Biography

Krasner emigrated from the Soviet Union to France and received in 1935 his PhD from the

University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...

under

Jacques Hadamard Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry, and partial differential equations. Biography The son of a tea ...

with thesis ''Sur la théorie de la ramification des idéaux de corps non-galoisiens de nombres algébriques''. From 1937 to 1960 he was a scientist at

CNRS The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

and from 1960 professor at the

University of Clermont-Ferrand The University of Clermont-Ferrand was officially founded in 1896, by merging of two existing faculties (Literature and Sciences) and a medical school. In 1976, due to political issues, the University split between University Clermont-Ferrand I - ...

. From 1965 he was a professor at the

University of Paris VI Pierre and Marie Curie University ( , UPMC), also known as Paris VI, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, ...

(Pierre et Marie Curie), where he retired in 1980 as professor emeritus. Krasner did research on

p-adic analysis In mathematics, ''p''-adic analysis is a branch of number theory that studies functions of ''p''-adic numbers. Along with the more classical fields of real and complex analysis, which deal, respectively, with functions on the real and complex ...

. In 1944 he introduced the concept of

ultrametric space In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to d(x,z)\leq\max\left\ for all x, y, and z. Sometimes the associated metric is also called a non-Archimedean metric or super-metric. Formal d ...

s,''Nombres semi-réels et espaces ultramétriques'', Comptes Rendus de l'Académie des Sciences, Tome II, vol. 219, p. 433 to which p-adic numbers belong. In 1951, alongside Lev Kaluznin, he proved the Krasner-Kaloujnine universal embedding theorem, which states that every extension of one group by another is isomorphic to a subgroup of the wreath product. A well-known Krasner's theorem, everywhere known as Krasner's lemma, relies the topological structure and the algebraic structure of vector spaces over local fields. In 1958 he received the Prix Paul Doistau–Émile Blutet of the

Académie des Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

Publications

* * * with Mirjana Vuković:

References

External links

Jean Dieudonne and Jean-Paul Pier on Marc Krasner, Cahiers Hist. Math. 1986
{{DEFAULTSORT:Krasner, Marc 20th-century French mathematicians 1912 births 1985 deaths Prix Paul Doistau–Émile Blutet laureates Soviet emigrants to France