Abstract
A ring R is called left (right) artinian if the set of all the left (right) ideals of R satisfies the dcc (descending chain condition) i.e. each strictly descending chain of left (right) ideals is finite (or equivalently, each non-void family of left (right) ideals contains a minimal element). Similarly, a ring is called left (right) noetherian if the set of all the left (right) ideals satisfies the acc (ascending chain condition).
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© 1998 Springer Science+Business Media Dordrecht
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Cǎlugǎreanu, G., Hamburg, P. (1998). Artinian and Noetherian Rings. In: Exercises in Basic Ring Theory. Kluwer Texts in the Mathematical Sciences, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9004-4_10
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DOI: https://doi.org/10.1007/978-94-015-9004-4_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4985-8
Online ISBN: 978-94-015-9004-4
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