Abstract
The exercises in this beginning section cover the basic aspects of rings, ideals (both 1-sided and 2-sided), zero-divisors and units, isomorphisms of modules and rings, the chain conditions, and Dedekind-finiteness. A ring R is said to be Dedekind-finite if ab = 1 in R implies that ba = 1. The chain conditions are the usual noetherian (ACC) or artinian (DCC) conditions which can be imposed on submodules of a module, or on 1-sided or 2-sided ideals of a ring.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Lam, T.Y. (1995). Wedderburn-Artin Theory. In: Exercises in Classical Ring Theory. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3987-9_1
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3987-9_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3989-3
Online ISBN: 978-1-4757-3987-9
eBook Packages: Springer Book Archive