The regular algebra of a poset

Pere Ara

doi:https://doi.org/10.1090/S0002-9947-09-04884-3

The regular algebra of a poset

Pere Ara

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

8 Citations (Scopus)

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
Pages (from-to)	1505-1546
Journal	Transactions of the American Mathematical Society
Volume	362
DOIs	https://doi.org/10.1090/S0002-9947-09-04884-3
Publication status	Published - 1 Mar 2010

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AB - 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.

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