Abstract
The Artinian condition on rings leads to a very satisfactory theory, at least in the semisimple case, yet it excludes such familiar examples as the ring of integers. This ring is included in the wider class of Noetherian rings, which has been much studied in recent years. We shall present some of the highlights, such as localization (Section 7.1), non-commutative principal ideal domains (Section 7.2) and Goldie’s theorem (Section 7.4), and illustrate the theory by examples from skew polynomial rings and power series rings in Section 7.3.
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© 2003 Professor P.M. Cohn
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Cohn, P.M. (2003). Noetherian rings and polynomial identities. In: Further Algebra and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-0039-3_7
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DOI: https://doi.org/10.1007/978-1-4471-0039-3_7
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1120-7
Online ISBN: 978-1-4471-0039-3
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