dc.contributor.author | Abrams, Gene | |
dc.contributor.author | Haefner, Jeremy | |
dc.contributor.author | Del Rio, Angel | |
dc.date.accessioned | 2009-07-29T19:04:19Z | |
dc.date.available | 2009-07-29T19:04:19Z | |
dc.date.issued | 1999 | |
dc.identifier.citation | Pacific Journal of Mathematics, vol. 187, no. 2, pp. 201-214, 1999 | en_US |
dc.identifier.uri | http://hdl.handle.net/1850/10344 | |
dc.description.abstract | Let P and P’ be finite preordered sets, and let R be a ring
for which the number of nonzero summands in a direct decomposition
of the regular module RR is bounded. We show
that if the incidence rings I(P;R) and I(P’;R) are isomorphic
as rings, then P and P' are isomorphic as preordered
sets. We give a stronger version of this result in case P and
P' are partially ordered. We show that various natural extensions
of these results fail. Specifically, we show that if
{Pj | j Є (omega) } is any collection of (locally finite) preordered
sets then there exists a ring S such that the incidence rings
{I(Pj, S) | j Є (omega) } are pairwise isomorphic. Additionally, we
verify that there exists a finite dimensional algebra R and locally
finite, nonisomorphic partially ordered sets P and P' for
which I(P;R) ~ I(P’;R). | en_US |
dc.language.iso | en_US | en_US |
dc.publisher | University of California | en_US |
dc.relation.ispartofseries | vol. 187 | en_US |
dc.relation.ispartofseries | no. 2 | en_US |
dc.title | The Isomorphism problem for incidence rings | en_US |
dc.type | Article | en_US |