Semisimple rings and Von Neumann regular rings of generalized power series

[摘要] 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 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.

[发布日期] 1997-12-15