Daniel Zelinsky (mathematician)

Last updated • 2 min readFrom Wikipedia, The Free Encyclopedia

Daniel Zelinsky (22 November 1922 – 16 September 2015) was an American mathematician, specializing in algebra.

Zelinsky studied at the University of Chicago with bachelor's degree in 1941. From 1941 to 1943 he was a research mathematician in Columbia University's applied mathematics group, in which he was the youngest member. [1] He was from 1943 to 1944 an instructor at the University of Chicago, where he received in 1943 his PhD under A. A. Albert with thesis Integral sets of quasiquaternion algebras. [2] Zelinsky worked from 1944 to 1946 for the applied mathematics group of Columbia University and from 1946 to 1947 as an instructor at the University of Chicago. From 1947 to 1949 he was at the Institute for Advanced Study as a National Research Council Fellow. At Northwestern University he became in 1949 an assistant professor, in the 1950s an associate professor, and in 1960 a full professor, retiring as professor emeritus in 1993. From 1975 to 1978 he was the chair of Northwestern University's mathematics department.[ citation needed ] He was a Guggenheim Fellow for the academic year 1955–1956, [3] which he spent at the Institute for Advanced Study. He was a visiting academic in 1960 at the University of California, Berkeley, in 1963 at Florida State University, in 1970–1971 at the Hebrew University of Jerusalem, and in 1979 at the Tata Institute.[ citation needed ] He was a co-editor of the collected works of A. A. Albert. [4] [5]

Dan Zelinsky's published work spans four decades and ranges across commutative and noncommutative rings, topological rings, topological methods in algebra, and cohomology, with Galois theory and Brauer groups being recurring themes. An especially significant chunk is his 10 paper collaboration with Alex Rosenberg from the mid-1950s to the early 1960s, including a paper in the famous Dimension Club series in the Nagoya Journal (On the Dimensions of Modules and Algebras VIII), in which they were joined by Samuel Eilenberg. [1]

Zelinsky was elected a Fellow of the American Association for the Advancement of Science in 1983 and was the chair or co-chair of the Association's Section A from 1984 to 1987.[ citation needed ]

His doctoral students include Andy Magid. [2]

Zelda Oser Zelinsky (1924–2015) was his wife; they married in September 1945. Upon his death he was survived by his widow, [6] a daughter, two sons, and four grandchildren.

Selected publications

Related Research Articles

<span class="mw-page-title-main">Alexander Grothendieck</span> French mathematician (1928–2014)

Alexander Grothendieck, later Alexandre Grothendieck in French, was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century.

Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions, possibly in some generalized sense. A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which does not always equal ; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions.

In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist Richard Brauer.

In ring theory and related areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative K-algebraA that is simple, and for which the center is exactly K.

Daniel Gray Quillen was an American mathematician. He is known for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.

<span class="mw-page-title-main">Richard Brauer</span> German-American mathematician

Richard Dagobert Brauer was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular representation theory.

In mathematics, a Severi–Brauer variety over a field K is an algebraic variety V which becomes isomorphic to a projective space over an algebraic closure of K. The varieties are associated to central simple algebras in such a way that the algebra splits over K if and only if the variety has a rational point over K. Francesco Severi studied these varieties, and they are also named after Richard Brauer because of their close relation to the Brauer group.

Abraham Adrian Albert was an American mathematician. In 1939, he received the American Mathematical Society's Cole Prize in Algebra for his work on Riemann matrices. He is best known for his work on the Albert–Brauer–Hasse–Noether theorem on finite-dimensional division algebras over number fields and as the developer of Albert algebras, which are also known as exceptional Jordan algebras.

<span class="mw-page-title-main">Melvin Hochster</span> American mathematician (born 1943)

Melvin Hochster is an American mathematician working in commutative algebra. He is currently the Jack E. McLaughlin Distinguished University Professor Emeritus of Mathematics at the University of Michigan.

In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of non-associative algebras, usually working over the real numbers. Over the real numbers, there are three such Jordan algebras up to isomorphism. One of them, which was first mentioned by Pascual Jordan, John von Neumann, and Eugene Wigner and studied by Albert (1934), is the set of 3×3 self-adjoint matrices over the octonions, equipped with the binary operation

<span class="mw-page-title-main">Ellis Kolchin</span> American mathematician (1916–1991)

Ellis Robert Kolchin was an American mathematician at Columbia University. He earned a doctorate in mathematics from Columbia University in 1941 under supervision of Joseph Ritt. Shortly after he served in the South Pacific in World War II. He was awarded a Guggenheim Fellowship in 1954 and 1961.

<span class="mw-page-title-main">Shimshon Amitsur</span> Israeli mathematician (1921–1994)

Shimshon Avraham Amitsur was an Israeli mathematician. He is best known for his work in ring theory, in particular PI rings, an area of abstract algebra.

In mathematics, Banach algebra cohomology of a Banach algebra with coefficients in a bimodule is a cohomology theory defined in a similar way to Hochschild cohomology of an abstract algebra, except that one takes the topology into account so that all cochains and so on are continuous.

<span class="mw-page-title-main">Alexander Merkurjev</span> Russian American mathematician (born 1955)

Aleksandr Sergeyevich Merkurjev is a Russian-American mathematician, who has made major contributions to the field of algebra. Currently Merkurjev is a professor at the University of California, Los Angeles.

In mathematics, a factor system is a fundamental tool of Otto Schreier’s classical theory for group extension problem. It consists of a set of automorphisms and a binary function on a group satisfying certain condition. In fact, a factor system constitutes a realisation of the cocycles in the second cohomology group in group cohomology.

In algebra, an SBI ring is a ring R such that every idempotent of R modulo the Jacobson radical can be lifted to R. The abbreviation SBI was introduced by Irving Kaplansky and stands for "suitable for building idempotent elements".

In mathematics, a biquaternion algebra is a compound of quaternion algebras over a field.

<span class="mw-page-title-main">Dmitry Fuchs</span> Russian-American mathematician

Dmitry Borisovich Fuchs is a Russian-American mathematician, specializing in the representation theory of infinite-dimensional Lie groups and in topology.

<span class="mw-page-title-main">Andy Magid</span> American mathematician

Andy Roy Magid is an American mathematician.

Yongbin Ruan is a Chinese mathematician, specializing in algebraic geometry, differential geometry, and symplectic geometry with applications to string theory.

References

  1. 1 2 Magid, Andy, ed. (1994). "Daniel Zelinsky: An Appreciation". Rings, extensions, and cohomology : proceedings of the Conference on the Occasion of the Retirement of Daniel Zelinsky. New York: Dekker. pp. ix–xii. ISBN   9780824792411.
  2. 1 2 Daniel Zelinsky at the Mathematics Genealogy Project
  3. "Daniel Zelinsky". John Simon Guggenheim Memorial Foundation.
  4. Albert, A. Adrian (1993), Block, Richard E.; Jacobson, Nathan; Osborn, J. Marshall; Saltman, David J.; Zelinsky, Daniel (eds.), Collected mathematical papers. Part 1. Associative algebras and Riemann matrices., Providence, R.I.: American Mathematical Society, ISBN   978-0-8218-0005-8, MR   1213451
  5. Albert, A. Adrian (1993), Block, Richard E.; Jacobson, Nathan; Osborn, J. Marshall; Saltman, David J.; Zelinsky, Daniel (eds.), Collected mathematical papers. Part 2. Nonassociative algebras and miscellany, Providence, R.I.: American Mathematical Society, ISBN   978-0-8218-0007-2, MR   1213452
  6. "Zelda Oser Zelinsky". Alumni and Friends of LaGuardia High School.
Daniel Zelinsky
Born22 November 1922
Died16 September 2015 (2015-09-17) (aged 92)
Awards Guggenheim Fellowship
Academic background
Alma mater University of Chicago
Doctoral advisor A. A. Albert