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Noetherian rings and polynomial identities

In: Further Algebra and Applications

Author

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  • P. M. Cohn

    (University College London, Department of Mathematics)

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.

Suggested Citation

  • P. M. Cohn, 2003. "Noetherian rings and polynomial identities," Springer Books, in: Further Algebra and Applications, chapter 7, pages 265-308, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4471-0039-3_7
    DOI: 10.1007/978-1-4471-0039-3_7
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