### 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 language | English |
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Pages (from-to) | 1505-1546 |

Journal | Transactions of the American Mathematical Society |

Volume | 362 |

DOIs | |

Publication status | Published - 1 Mar 2010 |

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## Cite this

Ara, P. (2010). The regular algebra of a poset.

*Transactions of the American Mathematical Society*,*362*, 1505-1546. https://doi.org/10.1090/S0002-9947-09-04884-3