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In mathematics, more specifically in abstract algebra, the Frobenius theorem, proved by Ferdinand Georg Frobenius in 1877, characterizes the finite-dimensional associative division algebras over the real numbers. According to the theorem, every such algebra is isomorphic to one of the following: R (the real numbers) C (the complex numbers) H ...
Vor 3 Tagen · Die axiomatische Behandlung der Determinante als Funktion von unabhängigen Variablen gab als erster Karl Weierstraß in seinen Berliner Vorlesungen (spätestens ab dem Jahre 1864 und möglicherweise schon davor), an die dann Ferdinand Georg Frobenius in seinen Berliner Vorlesungen des Sommersemesters 1874 anknüpfte und dabei unter anderem und vermutlich als erster den laplaceschen ...
Vor 2 Tagen · In fact, Ferdinand Georg Frobenius later proved in 1877 that for a division algebra over the real numbers to be finite-dimensional and associative, it cannot be three-dimensional, and there are only three such division algebras: , (complex numbers) and (quaternions) which have dimension 1, 2, and 4 respectively.
3. Mai 2024 · Matej Brešar. Frobenius' Theorem states that the only finite-dimensional real division algebras are the algebra of real numbers R, the algebra of complex numbers C, and the algebra of quaternions H. We present a short proof which uses only standard undergraduate mathematics.
Vor 6 Tagen · The Diophantine Frobenius Problem 2005-12-01 Jorge L. Ramírez Alfonsín During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he following problem, known as the Frobenius Problem (FP): given relatively prime positive
1. Mai 2024 · As of the 20th century, groups gained wide recognition by the pioneering work of Ferdinand Georg Frobenius and William Burnside (who worked on representation theory of finite groups), Richard Brauer's modular representation theory and Issai Schur's papers.
30. Apr. 2024 · Logarithmic geometry and Frobenius. Kazuya Kato, Chikara Nakayama, Sampei Usui. Based on the logarithmic algebraic geometry and the theory of Deligne systems, we define an abelian category of ℓ -adic sheaves with weight filtrations on a logarithmic scheme over a finite field, which is similar to the category of variations of mixed ...
