Heinz Prüfer (mathematician)

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Heinz Prüfer, 1930 in Jena

Ernst Paul Heinz Prüfer (born November 10, 1896 in Wilhelmshaven ; †  April 7, 1934 in Münster ) was a German mathematician who mainly dealt with algebra and group theory.

Live and act

Heinz Prüfer attended grammar school in Berlin-Zehlendorf and from 1915 studied at the Humboldt University in Berlin under Ferdinand Georg Frobenius , Hermann Amandus Schwarz , Paul Koebe and Issai Schur , from whom he received his doctorate in 1921 (Infinite Abelian Groups of Elements of Finite Order). He was then an assistant at the University of Hamburg and the University of Jena (with Koebe, where he completed his habilitation in 1923 and which he represented in teaching for two semesters in 1926/27) before becoming a private lecturer at the Westphalian Wilhelms University in Münster in 1927 . In 1930 he became an associate professor there. He died of lung cancer when he was only 37 . Behnke and Köthe characterize him in their obituary as reserved, very independent and careful (for example in his lectures).

In investigations into the decomposability of the countable primary Abelian groups (1923) he extended the basic set from finite Abelian groups to countable p-groups and introduced the concept of the examiner rank of a group. In Prüfer's theorem, he characterized countable groups, which can be represented as direct sums of groups of rank 1 (and gave counterexamples where this is not the case, the examiner group ). In Theory of Abelian Groups 1, 2 (1924/5) he generalized the results to modules on main ideal rings and introduced the concepts of the tester topology. Examiner also dealt with algebraic number theory , knot theory , Sturm-Liouville theory , the topological foundations of the theory of Riemannian surfaces and projective geometry .

The examiner codes are named after him, which he used in a new proof of the Cayley formula for listing tree graphs (Archive for Mathematics and Physics, Vol. 27, 1918, p. 742), as well as examiner rings or integrity areas . Examiner groups are also named after him.

Prüfer was married but had no children.

Fonts

  • Infinite Abelian groups of elements of finite order. 1921 (1923), doi : 10.18452 / 139 , (Berlin, University, dissertation, 1921).
  • Investigations into the decomposability of the countable primary Abelian groups. In: Mathematical Journal . Vol. 17, 1923, pp. 35-61 .
  • Abelian group theory. I. Basic characteristics. In: Mathematical Journal. Vol. 20, 1924, pp. 165-187 .
  • Abelian group theory. II. Ideal groups. In: Mathematical Journal. Vol. 22, 1925, pp. 226-253 .
  • New foundation of algebraic number theory. In: Mathematical Annals . Vol. 94, 1925, pp. 198-243 .
  • New derivation of the Sturm-Liouville series expansion of continuous functions. In: Mathematical Annals. Vol. 95, 1926, pp. 499-518 .
  • Projective geometry. Edited from the estate by Gerhard Fleddermann, Gottfried Köthe . Noske, Leipzig 1935, (2nd edition. With a foreword by Bartel L. van der Waerden . Geest and Portig, Leipzig 1953).

Web links

Remarks

  1. ↑ As a generalization of the situation in cyclic groups. The group has rank if each finite set of elements is part of an element-created subgroup, the smallest being such number.
  2. ↑ Commutative rings with one element, in which every finitely generated regular ideal is invertible.
personal data
SURNAME Examiner, Heinz
ALTERNATIVE NAMES Examiner, Ernst Paul Heinz (full name)
BRIEF DESCRIPTION German mathematician and university professor
DATE OF BIRTH November 10, 1896
PLACE OF BIRTH Wilhelmshaven
DATE OF DEATH April 7, 1934
Place of death Muenster