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Wedderburn-Artin Theory

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Part of the book series: Problem Books in Mathematics ((PBM))

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.

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© 1995 Springer Science+Business Media New York

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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

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  • 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

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