The regular algebra of a poset

Details The regular algebra of a poset The regular algebra of a poset

2008-05-16

arxiv.org/abs/0805.2563v2

Mathematics

Rings and Algebras

47 pages. Revised version, to appear in Trans. Amer. Math. Soc

Scientific paper

Let $K$ be a field. We attach to each finite poset $\mathbb P$ a von Neumann regular $K$-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 $p=p+q$ whenever $q

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