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Zbl 0908.16001
Kleiner, Israel
From numbers to rings: The early history of ring theory. (English)
[J] Elem. Math. 53, No.1, 18-35 (1998). ISSN 0013-6018; ISSN 1420-8962/e

In this history of ring theory, going roughly from 1840 to 1940, the author lists the main stages: in the non-commutative theory they are hypercomplex systems and division algebras, while the commutative theory has the two large branches of algebraic number theory and algebraic geometry, with a brief mention of some of the methods to which they gave arise. There is no mention of more modern developments, nor of the many applications: representation theory, power series rings in probability theory, algebras in functional analysis etc.
[P.M.Cohn (London)]

MSC 2000:: *16-03 Historical (assoc. rings and algebras)
01A55 Mathematics in the 19th century
01A60 Mathematics in the 20th century

Keywords: hypercomplex systems; division algebras; algebraic number theory; algebraic geometry

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