History
Commutative ring theory originated in algebraic number theory, algebraic geometry, and invariant theory. Central to the development of these subjects were the rings of integers in algebraic number fields and algebraic function fields, and the rings of polynomials in two or more variables. Noncommutative ring theory began with attempts to extend the complex numbers to various hypercomplex number systems. The genesis of the theories of commutative and noncommutative rings dates back to the early 19th century, while their maturity was achieved only in the third decade of the 20th century.
More precisely, William Rowan Hamilton put forth the quaternions and biquaternions; James Cockle presented tessarines and coquaternions; and William Kingdon Clifford was an enthusiast of split-biquaternions, which he called algebraic motors. These noncommutative algebras, and the non-associative Lie algebras, were studied within universal algebra before the subject was divided into particular mathematical structure types. One sign of re-organization was the use of direct sums to describe algebraic structure.
The various hypercomplex numbers were identified with matrix rings by Joseph Wedderburn (1908) and Emil Artin (1928). Wedderburn's structure theorems were formulated for finite-dimensional algebras over a field while Artin generalized them to Artinian rings.
Read more about this topic: Ring Theory
Famous quotes containing the word history:
“Most events recorded in history are more remarkable than important, like eclipses of the sun and moon, by which all are attracted, but whose effects no one takes the trouble to calculate.”
—Henry David Thoreau (1817–1862)
“It is my conviction that women are the natural orators of the race.”
—Eliza Archard Connor, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 4, ch. 9, by Susan B. Anthony and Ida Husted Harper (1902)
“No event in American history is more misunderstood than the Vietnam War. It was misreported then, and it is misremembered now.”
—Richard M. Nixon (b. 1913)