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Semisimple Rings and Von Neumann Regular Rings of Generalized Power Series

✍ Scribed by Paulo Ribenboim

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 213 KB
Volume: 198
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7063

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✦ Synopsis

In this paper we continue our investigation of generalized power series. The main theorem determines rings of generalized power series which are Von Neumann regular rings and semisimple rings. In the final section we give a new proof of Neumann's theorem on skewfields of generalized power series with totally ordered group of exponents. Using a result of w x Erdos and Rado, we deduce a simple proof of a theorem in 1 , which is ¨proven here also for skewfields.

It is my pleasure to thank C. U. Jensen and K. R. Goodearl for useful comments while this paper was in preparation.

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Ž . 1.1 An ordered set S, F is finite if and only if it is noetherian, artinian, and narrow.

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