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Amitsur
Shimshon Avraham Amitsur (born Kaplan; he, שמשון אברהם עמיצור; August 26, 1921 – September 5, 1994) was an Israeli mathematician. He is best known for his work in ring theory, in particular PI rings, an area of abstract algebra. Biography Amitsur was born in Jerusalem and studied at the Hebrew University under the supervision of Jacob Levitzki. His studies were repeatedly interrupted, first by World War II and then by the 1948 Arab–Israeli War. He received his M.Sc. degree in 1946, and his Ph.D. in 1950. Later, for his joint work with Levitzki, he received the first Israel Prize in Exact Sciences. He worked at the Hebrew University until his retirement in 1989. Amitsur was a visiting scholar at the Institute for Advanced Study from 1952 to 1954. He was an Invited Speaker at the ICM in 1970 in Nice. He was a member of the Israel Academy of Sciences, where he was the Head for Experimental Science Section. He was one of the founding editors of the ''Israe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amitsur–Levitzki Theorem
In algebra, the Amitsur–Levitzki theorem states that the algebra of ''n'' × ''n'' matrices over a commutative ring satisfies a certain identity of degree 2''n''. It was proved by . In particular matrix rings are polynomial identity rings such that the smallest identity they satisfy has degree exactly 2''n''. Statement The standard polynomial of degree ''n'' is :S_n(x_1,\dots,x_n) = \sum_\text(\sigma)x_ \cdots x_ in non-commuting variables ''x''1, ..., ''x''''n'', where the sum is taken over all ''n''! elements of the symmetric group ''S''''n''. The Amitsur–Levitzki theorem states that for ''n'' × ''n'' matrices ''A''1, ..., ''A''2''n'' whose entries are taken from a commutative ring then :S_(A_1,\dots,A_) = 0. Proofs gave the first proof. deduced the Amitsur–Levitzki theorem from the Koszul–Samelson theorem about primitive cohomology of Lie algebras. and gave a simple combinatorial proof as follows. By linearity it is enough to pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Levitzki
Jacob Levitzki, also known as Yaakov Levitsky ( he, יעקב לויצקי) (17 August 1904 - 25 February 1956) was an Israeli mathematician. Biography Levitzki was born in 1904 in the Russian Empire and emigrated to then Ottoman-ruled Palestine in 1912. After completing his studies at the Herzliya Gymnasia, he travelled to Germany and, in 1929, obtained a doctorate in mathematics from the University of Göttingen under the supervision of Emmy Noether. In 1931, after two years at Yale University, in New Haven, Connecticut, Levitzki returned to Palestine to join the faculty at the Hebrew University of Jerusalem. Awards Levitzki together with Shimshon Amitsur, who had been one of his students at the Hebrew University, were each awarded the Israel Prize in exact sciences in 1953, the inaugural year of the prize, for their work on the laws of noncommutative rings. Levitzki's son Alexander Levitzki, a recipient of the Israel Prize in 1990, in life sciences, established the Levitzki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Israel Prize Recipients
This is a complete list of recipients of the Israel Prize from the inception of the Prize in 1953 through to 2022. List For each year, the recipients are, in most instances, listed in the order in which they appear on the official Israel Prize website. Note: The table can be sorted chronologically (default), alphabetically or by field utilizing the icon. See also * List of Israeli Nobel laureates References External links * Listat the Jewish Virtual Library 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""Th ... {{DEFAULTSORT:List Of Israel Prize Recipients Israel Prize winners Israel Prize winners de:Israel-Preis#Die Preisträger ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aner Shalev
Aner Shalev (born 24 January 1958) is a professor at the Einstein Institute of Mathematics at the Hebrew University of Jerusalem, and a writer. Biography Shalev was born in Kibbutz Kinneret and grew up in Beit Berl. He moved to Jerusalem at 18 to study mathematics and philosophy at the Hebrew University, and since then, excluding some years abroad, he has been living mainly in Jerusalem. Shalev received his Ph.D. in mathematics at the Hebrew University in 1989, summa cum laude. His doctoral thesis was written under the supervision of Professors Amitsur and Mann and dealt with group rings, an area combining group theory and ring theory. Shalev spent his post-doctoral period at Oxford University and at the University of London, returned to Israel in 1992, when he was hired as a senior lecturer at the Hebrew University. Shalev was appointed full professor in 1996, and spent sabbaticals at the Universities of Chicago, Oxford (All Souls College), and London (Imperial College). H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PI Ring
In ring theory, a branch of mathematics, a ring ''R'' is a polynomial identity ring if there is, for some ''N'' > 0, an element ''P'' ≠ 0 of the free algebra, Z, over the ring of integers in ''N'' variables ''X''1, ''X''2, ..., ''X''''N'' such that :P(r_1, r_2, \ldots, r_N) = 0 for all ''N''- tuples ''r''1, ''r''2, ..., ''r''''N'' taken from ''R''. Strictly the ''X''''i'' here are "non-commuting indeterminates", and so "polynomial identity" is a slight abuse of language, since "polynomial" here stands for what is usually called a "non-commutative polynomial". The abbreviation PI-ring is common. More generally, the free algebra over any ring ''S'' may be used, and gives the concept of PI-algebra. If the degree of the polynomial ''P'' is defined in the usual way, the polynomial ''P'' is called monic if at least one of its terms of highest degree has coefficient equal to 1. Every commutative ring is a PI-ring, satisfying the polynomial identity ''XY'' − ''YX'' = 0. Therefore, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
