Jakob Levitzki

Jakob Levitzki , also Jacob Levitzki , Yaakov Levitsky ( Hebrew יעקב לויצקי; *  August 17, 1904 in Cherson , Ukraine ; † 1956 in Jerusalem ) was an Israeli mathematician who studied algebra .

Career

The family moved to Palestine in 1913, where Levitzki attended the Hebrew High School in Tel Aviv . From 1922 he studied mathematics at the University of Göttingen (and one semester at the University of Cologne ), where he received his doctorate with distinction from Emmy Noether (and Edmund Landau ) in 1929 ( On completely reducible rings and their sub-rings , Nachrichten Göttinger Ges. Wiss., 1929 , P. 240, Mathematische Zeitschrift, Vol. 33, 1931, p. 663). In 1928/29 he was an assistant at the University of Kiel and in 1929/30 as a sterling scholar at Yale University . In 1931 he returned to Israel and became a professor at the Hebrew University of Jerusalem .

In 1954 he received the Israel Prize . Levitzki is considered to be the founder of algebra research in Israel.

The Amitsur-Levitzki theorem states that the sum (over all permutations of 1, ..., 2k with the Signum sign of the permutation ) of the products of any 2k (kxk) matrices (defined by a commutative ring) ${\displaystyle \sigma }$ ${\displaystyle \sigma }$ ${\displaystyle A_{j}\,(1\leq j\leq 2k)}$

${\displaystyle \sum \mathrm {sign} (\sigma _{i})\prod A_{\sigma _{i}(j)}=0.}$

In other words: for the ring of (k × k) matrices over a commutative ring, the standard polynomial of degree 2k fulfills a polynomial identity. The theorem also states that no polynomial of minor degree satisfies a polynomial identity in these rings. The theorem is the starting point of the theory of rings with polynomial identity.

Independently of Charles Hopkins , he proved a theorem, which was surprising at the time, in 1939, that the descending chain condition in rings results in the ascending chain condition in many cases, today cited as the Hopkins-Levitzki theorem, after it was previously mostly named after Hopkins, as this was in in a leading US journal, Levitzki in Compositio Mathematica, which was little read in the US at the time . The American mathematician Carl Faith said in his autobiographical and historical book on ring theory that, in order to give Levitzki satisfaction, he later named certain rings after him.

His son Alexander Levitzki is a professor of biochemistry at the Hebrew University and also received the Israel Prize. In memory of his parents, he donated the Levitzki Prize for Algebra in Israel.

Shimshon Amitsur (1948) is one of his students .

literature

• Shimshon Amitsur, Israel Journal of Mathematics, Vol. 19, 1974, p. 1

swell

• Renate Tobies : Biographical lexicon in mathematics for post-doctoral students. At German universities and technical colleges. WS 1907/08 to WS 1944/45 . Rauner Verlag, Augsburg 2006, ISBN 3-936905-21-5 , ( Algorism 58).
• The Amitsur-Levitzki Theorem for a Non Mathematician - Gil Kalai zum Amitsur-Levitzki Theorem, May 12, 2009 (English)
• Amitsur-Levitzki theorem (Amitsur-Levitzki theorem) at the Encyclopaedia of Mathematics (English)
• Levitzki Prize פרס לויצקי - Short biography on the Levitzki Prize page (English and Hebrew; with picture)

References

1. ↑ First he wanted to study chemistry, after a lecture by Emmy Noether he switched to mathematics
2. ^ Award of the Levitzki Prize, Israeli Mathematical Union
3. ↑ Amitsur, Levitzki: Minimal identities for algebras , Proc. AMS, Vol. 1, 1950, pp. 449-463. There is other evidence as well, for example Razmyslov reduced the theorem to the Cayley-Hamilton theorem. Richard Swan gave a graph theoretical proof in 1963.
4. ^ Carl Faith: Rings and things and a fine array of twentieth century associative algebra , AMS, 2nd edition 2004, p. 340