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arXiv 0802.18722008-02math.RA

von Neumann正则环的实现问题

The realization problem for von Neumann regular rings

Pere Ara

备注：: 15 pages, survey paper. It contains a new version of Proposition 4.1, due to Ken Goodearl
发表信息：: Ring Theory 2007. Proceedings of the Fifth China-Japan-Korea Conference, (eds. H. Marubayashi, K. Masaike, K. Oshiro, M. Sato); World Scientific, 2009, pp. 21--37

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摘要：

综述了von Neumann正则环的实现问题的最新进展，该问题是：在von Neumann正则环$R$上，每个可数的锥加细么半群是否都能实现为环上的可生成的投射右$R$ -模的类的么半群.

英文摘要：

We survey recent progress on the realization problem for von Neumann regular rings, which asks whether every countable conical refinement monoid can be realized as the monoid of isoclasses of finitely generated projective right $R$-modules over a von Neumann regular ring $R$.

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