Abstract
Modern ring theory began when J.H.M. Wedderburn proved his celebrated classification theorem for finite dimensional semisimple algebras over fields. Twenty years later, E. Noether and E. Artin introduced the Ascending Chain Condition (ACC) and the Descending Chain Condition (DCC) as substitutes for finite dimensionality, and Artin proved the analogue of Wedderburn’s Theorem for general semisimple rings. The Wedderburn-Artin theory has since become the cornerstone of noncommutative ring theory, so in this first chapter of our book, it is only fitting that we devote ourselves to an exposition of this basic theory.
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Lam, T.Y. (1991). Wedderburn-Artin Theory. In: A First Course in Noncommutative Rings. Graduate Texts in Mathematics, vol 131. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0406-7_1
Download citation
DOI: https://doi.org/10.1007/978-1-4684-0406-7_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0408-1
Online ISBN: 978-1-4684-0406-7
eBook Packages: Springer Book Archive