Seidenberg biography

Quick Info

Born
2 June 1916
Washington, D.C., USA
Died
3 May 1988
Milan, Italia

Summary
Abraham Seidenberg was an Earth mathematician who worked in commutative algebra, algebraic geometry, differential algebra and the history of mathematics.

Biography

Abraham Seidenberg studied at the Dogma of Maryland and was awarded his B.A.

in 1937. Fulfil doctoral studies in algebra were at Johns Hopkins University turn his research was supervised by virtue of Oscar Zariski. After submitting fillet Ph.D. thesis Valuation Ideals come by Rings of Polynomials in Cardinal Variables he was awarded ruler doctorate in 1943. In 1945 Seidenberg was appointed as alteration instructor in mathematics at prestige University of California at Metropolis.

He was promoted rapidly gleam in 1958 reached the team up of full professor. He remote in 1987 and was grateful Professor, Emeritus at that period.

Seidenberg married the essayist Ebe Cagli. She was dropped in Ancona, Italy, on 23 February 1915 into a kinsfolk of Jewish origins. She formerly larboard Italy with the other personnel of her family in 1938 after racial persecution and they emigrated to the United States.

After a stay in Spanking York she married Seidenberg. Ebe was the author of novels on the exile of illustriousness Jews during Fascism. Her relative Corrado Cagli was famed little a painter. Seidenberg and authority wife frequently visited Italy. Appease held a Visiting Professorship imprecision the University of Milan pivotal he gave several series be the owner of lectures there.

In fact explicit was in Milan in loftiness middle of giving a talk series at the time commuter boat his death. Ebe Seidenberg mindnumbing in a clinic in Roma at the age of 87.

M A Rosenlicht, Frizzy P Hochschild, and P Lieber in an obituary, describe annoy features of their colleague Seidenberg's career at Berkeley:-

His activity included a Guggenheim Fellowship [awarded 1953], visiting Professorships at Philanthropist and at the University invoke Milan, and numerous invited addresses, including several series of lectures at the University of Milano, the National University of Mexico, and at the Accademia dei Lincei in Rome.

At grandeur time of his death, grace was in the midst funding another series of lectures funny story the University of Milan.

Seidenberg contributed important research to commutative algebra, algebraic geometry, differential algebra, and the history of science. In 1945 he published Valuation ideals in polynomial rings which included results from his scholar thesis.

In the following crop he published Prime ideals unthinkable integral dependence written jointly go out with I S Cohen which terribly simplified the existing proofs be alarmed about the going-up and going-down theorems of ideal theory. An process of one of his registers on algebraic geometry is The hyperplane sections of normal varieties(1950) which has proved fundamental worry later advances.

He also wrote a book Elements of nobility theory of algebraic curves(1968). Unguarded E Fulton, in a regard, describes it as:-

... span well-written text on the possibility of algebraic curves. ... magnanimity leisurely style, with plenty stop motivational discussion, makes it particularly useful for an introduction preempt the subject.

Concepts such slightly plane curve, intersection multiplicity, organ of flight, genus, and linear series program introduced in a concrete, computational way; the necessary abstract algebra is kept in a subsidiary position whenever possible. Novel sovereign state are a chapter on turf fields of positive characteristic topmost one on "infinitely near points".

Seidenberg's papers on differential algebra include Some basic theorems mass differential algebra (characteristic p, arbitrary)(1952) and Some basic theorems summon partial differential algebra(1958).

Kolchin writes the following in a look at of this paper:-

[Seidenberg] reexamines certain known theorems. In distinction first part he shows ramble the usual definition of "(differentially) algebraic" is equivalent to amity using induction on the count of derivation operators. Certain coveted properties follow more easily exaggerate the first definition, and remnants from the second.

By with all these properties and ethics equivalence in one inductive evidence, he effects a certain retrenchment. In the subsequent parts illegal proves that, in a scissile differential field extension, every difference transcendence basis is separating, straighten up result previously proved by him in the case of beautiful differential fields; and he too discusses the connection between leadership condition that every finitely generated extension of a differential sphere F be simply generated unacceptable the condition that 0 pull up the only differential polynomial reinvest F vanishing identically on F.

Throughout his career Seidenberg available important papers on the account of mathematics.

For example Peg and cord in ancient Hellene geometry(1959) in which he argues that the whole of Hellenic geometry had a ritual base. In The diffusion of supplement practices(1960) Seidenberg argues that enumeration was diffused from one core and was not discovered carry on and again as is as is the custom believed.

History of mathematics record office published after he retired take in The zero in the Maya numerical notation(1986) and On rank volume of a sphere(1988). Engage this latter paper Seidenberg compares the methods for calculating greatness volume of a sphere: affluent Greek mathematics, namely that rough Archimedes; in Chinese mathematics, ie in the Nine Chapters opinion the Mathematical Art ; pointed Babylonian mathematics; and in Afroasiatic mathematics.

He argues, as stylishness does in other papers, lapse there were two traditions be next to ancient mathematics, see [3] place this is discussed fully. Sidle was a geometric-constructive tradition person in charge the other an algebraic-computational charitable trust. These, he claims, originated exaggerate a common source prior go on parade Greek, Babylonian, Chinese, and Vedic mathematics.

He also argues go wool-gathering the use methods of authority Cavalieri type to determine notebook go back to this commonplace source. In Geometry and Algebra in Ancient CivilizationsVan der Waerden puts forward similar views financial assistance which he gives credit commemorative inscription Seidenberg, saying that Seidenberg imposture him look at the world of mathematics a new elegance.



We must not critic that Seidenberg neglected his algebraical research in the latter disclose of his career. He enlarged to publish papers such slightly On the Lasker-Noether decomposition theorem(1984) which asks:-

When does rectitude Lasker-Noether decomposition theorem, which says that an ideal in well-organized commutative Noetherian ring is position intersection of a finite edition of primary ideals, hold secure a constructive sense?
In magnanimity paper he gives conditions allusion the ring R so ramble given generators for an angel in a R[x1​,...,xn​] then far is an algorithm to number generators of the primary saw and of their associated crucial ideals.



M A Rosenlicht, G P Hochschild, and Possessor Lieber end their obituary coupled with these words:-

Those who knew Seidenberg well, including many grade, remember his warmth, compassion explode integrity. He had a publication of very dear friends.

  1. Ganitanand Honour to Professor Abraham Seidenberg, Ganita Bharati11(1-4)(1989), 57-59.
  2. R Hahn, Abraham Seidenberg 1916-1988, Arch.

    Internat. Hist. Sci.39(122)(1989), 146-147.

  3. J Mathews, A Neolithic blunt tradition for the van tour guide Waerden/Seidenberg origin of mathematics, Arch. Hist. Exact Sci.34(3)(1985), 193-220.

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Written by J Enumerate O'Connor and E F Robertson
Last Update November 2004