Ernst Paul Heinz Prüfer (10 November 1896 – 7 April 1934) was a

German German(s) may refer to: * Germany (of or related to) ** Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ge ...

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

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, structure, space, models, and change. History On ...

born in

Wilhelmshaven Wilhelmshaven (, ''Wilhelm's Harbour''; Northern Low Saxon: ''Willemshaven'') is a coastal town in Lower Saxony, Germany. It is situated on the western side of the Jade Bight, a bay of the North Sea, and has a population of 76,089. Wilhelmsh ...

. His major contributions were on

abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is comm ...

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

, algebraic numbers, knot theory and Sturm–Liouville theory. In 1915 he began his University studies in Mathematics,

Physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

and Chemistry in

Berlin Berlin ( , ) is the capital and List of cities in Germany by population, largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's List of cities in the European Union by population within ci ...

. After that he started his Doctorate degree with

Issai Schur Issai Schur (10 January 1875 – 10 January 1941) was a Russian mathematician who worked in Germany for most of his life. He studied at the University of Berlin. He obtained his doctorate in 1901, became lecturer in 1903 and, after a stay at th ...

as his advisor at Friedrich Wilhelm University, Berlin. In 1921 he obtained his Doctorate degree. His thesis was named ''Unendliche Abelsche Gruppen von Elementen endlicher Ordnung'' (Infinite abelian groups of elements of finite order). This thesis set the road for his contributions on abelian groups. In 1922 he worked with mathematician

Paul Koebe Paul Koebe (15 February 1882 – 6 August 1945) was a 20th-century German mathematician. His work dealt exclusively with the complex numbers, his most important results being on the uniformization of Riemann surfaces in a series of four papers in ...

in the

University of Jena The University of Jena, officially the Friedrich Schiller University Jena (german: Friedrich-Schiller-Universität Jena, abbreviated FSU, shortened form ''Uni Jena''), is a public research university located in Jena, Thuringia, Germany. The un ...

, and in 1923 he obtained tenure and was at this University until 1927. In that year he moved to Münster University where he worked until the end of his life. His final work was about

projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, ...

, but it was posthumously completed by his students Gustav Fleddermann and Gottfried Köthe. Heinz Prüfer was married, but never had children. He died prematurely at 37 years of age in 1934 in Münster Germany, due to lung cancer.

Mathematical contributions

Heinz Prüfer created the following mathematical notions that were later named after him: *

Prüfer sequence In combinatorial mathematics, the Prüfer sequence (also Prüfer code or Prüfer numbers) of a labeled tree is a unique sequence associated with the tree. The sequence for a tree on ''n'' vertices has length ''n'' − 2, and can be ...

(also known as a Prüfer code; it has broad applications in

and network theory). *

Prüfer domain In mathematics, a Prüfer domain is a type of commutative ring that generalizes Dedekind domains in a non-Noetherian context. These rings possess the nice ideal and module theoretic properties of Dedekind domains, but usually only for finitely gen ...

. Also see

Bézout domain In mathematics, a Bézout domain is a form of a Prüfer domain. It is an integral domain in which the sum of two principal ideals is again a principal ideal. This means that for every pair of elements a Bézout identity holds, and that every fini ...

, which is a Prüfer domain *

Prüfer rank In mathematics, especially in the area of algebra known as group theory, the Prüfer rank of a pro-p group measures the size of a group in terms of the ranks of its elementary abelian sections.. The rank is well behaved and helps to define analytic ...

Prüfer manifold In mathematics, the Prüfer manifold or Prüfer surface is a 2-dimensional Hausdorff real analytic manifold that is not paracompact. It was introduced by and named after Heinz Prüfer. Construction The Prüfer manifold can be constructed as ...

also known as Prüfer surface or Prüfer analytical manifold *

Prüfer group In mathematics, specifically in group theory, the Prüfer ''p''-group or the ''p''-quasicyclic group or ''p''∞-group, Z(''p''∞), for a prime number ''p'' is the unique ''p''-group in which every element has ''p'' different ''p''-th roots. ...

* Prüfer theorems

References

* * *
Jürgen Elstrodt and Norbert Schmitz: History of Münster University (2013). Chapter 52. page 111, Heinz Prüfer Biographie. Chapter 52. page 111
* * * * * *

External links

* * {{DEFAULTSORT:Prufer, Ernst Paul Heinz 1896 births 1934 deaths 20th-century German mathematicians 19th-century German Jews Academic staff of the University of Münster People from Wilhelmshaven