Richard Dedekind's major contribution was a redefinition of irrational numbers in terms of Dedekind cuts. He introduced the notion of an ideal in ring theory. He was born in Braunschweig on 6 October 1831 and died there on 12 February 1916. In 1871 he introduced the German word Körper for a field of numbers closed under the four arithmetic operations, and he is credited with the Dedekind cut, the ideal and the early study of the modular group alongside Felix Klein.
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Source Abstract Algebra (Wikipedia)
Source Field (mathematics) (Wikipedia)
Source Wikipedia: Modular group
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Source Richard Dedekind, Biography (MacTutor History of Mathematics)
Source Richard Dedekind, Biography (MacTutor History of Mathematics)
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Source Richard Dedekind, Biography (MacTutor History of Mathematics)Quick InfoQuote, Quick Info
Born 6 October 1831 Braunschweig, duchy of Braunschweig (now Germany)
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1. Richard Dedekind, Biography (MacTutor History of Mathematics)
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Richard Dedekind 's major contribution was a redefinition of irrational numbers in terms of Dedekind cuts. He introduced the notion of an ideal in Ring Theory.
Field (mathematics) (Wikipedia)
Wikimedia FoundationAttributed Works: Field (Abstract Algebra), LeadQuote, Attributed Works: Field (Abstract Algebra), Lead
In 1871 Richard Dedekind introduced, for a set of real or complex numbers that is closed under the four arithmetic operations, the German word Körper, which means "body" or "corpus" (to suggest an organically closed entity)
Abstract Algebra (Wikipedia)
Wikimedia FoundationAttributed Works: Algebraic Structure, LeadQuote, Attributed Works: Algebraic Structure, Lead
Dedekind and Miller independently characterized Hamiltonian groups and introduced the notion of the commutator of two elements
Wikipedia: Modular group
Attributed Works: Modular Group, LeadQuote, Attributed Works: Modular Group, Lead
The modular group and its subgroups were first studied in detail by Richard Dedekind and by Felix Klein as part of his Erlangen programme in the 1870s.
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