The Isomorphism problem for incidence rings
View/ Open
Date
1999Author
Abrams, Gene
Haefner, Jeremy
Del Rio, Angel
Metadata
Show full item recordAbstract
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).
Collections
The following license files are associated with this item: