Heinz Prüfer
Encyclopedia
Ernst Paul Heinz Prüfer (10 November 1896–7 April 1934) was a German mathematician
, who worked on abelian group
s, algebraic number
s, knot theory
and Sturm-Liouville theory
. His advisor was Issai Schur
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, who worked on abelian group
Abelian group
In abstract algebra, 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 their order . Abelian groups generalize the arithmetic of addition of integers...
s, algebraic number
Algebraic number
In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients. Numbers such as π that are not algebraic are said to be transcendental; almost all real numbers are transcendental...
s, knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
and Sturm-Liouville theory
Sturm-Liouville theory
In mathematics and its applications, a classical Sturm–Liouville equation, named after Jacques Charles François Sturm and Joseph Liouville , is a real second-order linear differential equation of the form...
. His advisor was Issai Schur
Issai Schur
Issai Schur was a mathematician who worked in Germany for most of his life. He studied at Berlin...
.
See also
- Prüfer manifoldPrüfer manifoldIn 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 follows...
- Prüfer sequencePrüfer sequenceIn combinatorial mathematics, the Prüfer sequence 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 generated by a simple iterative algorithm...
(also known as Prüfer code). - Prüfer rankPrüfer rankIn 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 pro-p-groups...
- Prüfer groupPrüfer groupIn mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p∞-group, Z, for a prime number p is the unique p-group in which every element has p pth roots. The group is named after Heinz Prüfer...
- Prüfer domainPrüfer domainIn 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 generated modules...
- Prüfer theoremsPrüfer theoremsIn mathematics, two Prüfer theorems, named after Heinz Prüfer, describe the structure of certain infinite abelian groups. They have been generalized by L. Ya. Kulikov.- Statement :Let A be an abelian group...