Noetherian rings and polynomial identities

P. M. Cohn
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P. M. Cohn: University College London, Department of Mathematics

Chapter 7 in Further Algebra and Applications, 2003, pp 265-308 from Springer

Abstract: 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.

Keywords: Integral Domain; Polynomial Ring; Division Algebra; Polynomial Identity; Regular Element (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-1-4471-0039-3_7

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