History
The concept of field was used implicitly by Niels Henrik Abel and Évariste Galois in their work on the solvability of equations.
In 1871, Richard Dedekind, called a set of real or complex numbers which is closed under the four arithmetic operations a "field".
In 1881, Leopold Kronecker defined what he called a "domain of rationality", which is indeed a field of polynomials in modern terms.
In 1893, Heinrich M. Weber gave the first clear definition of an abstract field.
In 1910 Ernst Steinitz published the influential paper Algebraische Theorie der Körper (German: Algebraic Theory of Fields). In this paper he axiomatically studied the properties of fields and defined many important field theoretic concepts like prime field, perfect field and the transcendence degree of a field extension.
Galois, who did not have the term "field" in mind, is honored to be the first mathematician linking group theory and field theory. Galois theory is named after him. However it was Emil Artin who first developed the relationship between groups and fields in great detail during 1928-1942.
Read more about this topic: Field Theory (mathematics)
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