The regular algebra of a poset

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Abstract

Let K be a fixed field. We attach to each finite poset ℙ avon Neumann regular K-algebra Qk (ℙ) in a functorial way. We show that the monoid of isomorphism classes of finitely generated projective Qk (ℙ)-modules is the abelian monoid generated by ℙ with the only relations given by p = p + q whenever q< p in ℙ. This extends the class of monoids for which there is a positive solution to the realization problem for von Neumann regular rings. © 2009 American Mathematical Society.
Original languageEnglish
Pages (from-to)1505-1546
JournalTransactions of the American Mathematical Society
Volume362
DOIs
Publication statusPublished - 1 Mar 2010

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