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ISSN 1088-6850(e) ISSN 0002-9947(p)

The regular algebra of a poset

Author(s): Pere Ara
Journal: Trans. Amer. Math. Soc. 362 (2010), 1505-1546.
MSC (2000): Primary 16D70; Secondary 16E50, 06F05, 46L80
Posted: October 20, 2009
MathSciNet review: 2563739
Retrieve article in: PDF

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Abstract: Let be a fixed field. We attach to each finite poset $\mathbb{P}$ a von Neumann regular -algebra $Q_K(\mathbb{P})$ in a functorial way. We show that the monoid of isomorphism classes of finitely generated projective $Q_K(\mathbb{P})$ -modules is the abelian monoid generated by $\mathbb{P}$ with the only relations given by whenever in $\mathbb{P}$ . This extends the class of monoids for which there is a positive solution to the realization problem for von Neumann regular rings.

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