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, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

) was a Russian Empire-born French mathematician, who worked on algebraic number theory. Krasner emigrated from the Soviet Union to France and received in 1935 his PhD from the

University of Paris , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

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 teac ...

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 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 (french: link=no, Université Pierre-et-Marie-Curie, UPMC), also known as Paris 6, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the L ...

(Pierre et Marie Curie), where he retired in 1980 as professor emeritus. Krasner did research on p-adic analysis. 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\. Sometimes the associated metric is also called a non-Archimedean metric or super-metric. Although some of the theorems ...

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 The Prix Paul Doistau–Émile Blutet is a biennial prize awarded by the French Academy of Sciences in the fields of mathematics and physical sciences since 1954. Each recipient receives 3000 euros. The prize is also awarded quadrennially in bio ...

of the

Académie des Sciences The French Academy of Sciences (French: ''Académie des 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 research. It was at th ...

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