History
The subject, first known as ideal theory, began with Richard Dedekind's work on ideals, itself based on the earlier work of Ernst Kummer and Leopold Kronecker. Later, David Hilbert introduced the term ring to generalize the earlier term number ring. Hilbert introduced a more abstract approach to replace the more concrete and computationally oriented methods grounded in such things as complex analysis and classical invariant theory. In turn, Hilbert strongly influenced Emmy Noether, to whom we owe much of the abstract and axiomatic approach to the subject. Another important milestone was the work of Hilbert's student Emanuel Lasker, who introduced primary ideals and proved the first version of the Lasker–Noether theorem.
Much of the modern development of commutative algebra emphasizes modules. Both ideals of a ring R and R-algebras are special cases of R-modules, so module theory encompasses both ideal theory and the theory of ring extensions. Though it was already incipient in Kronecker's work, the modern approach to commutative algebra using module theory is usually credited to Emmy Noether.
Read more about this topic: Commutative Algebra
Famous quotes containing the word history:
“The history of modern art is also the history of the progressive loss of art’s audience. Art has increasingly become the concern of the artist and the bafflement of the public.”
—Henry Geldzahler (1935–1994)
“No matter how vital experience might be while you lived it, no sooner was it ended and dead than it became as lifeless as the piles of dry dust in a school history book.”
—Ellen Glasgow (1874–1945)
“I believe that history has shape, order, and meaning; that exceptional men, as much as economic forces, produce change; and that passé abstractions like beauty, nobility, and greatness have a shifting but continuing validity.”
—Camille Paglia (b. 1947)