Weak multiplication modules over a pullback of Dedekind domains
Volume 114 / 2009
Colloquium Mathematicum 114 (2009), 99-112
MSC: 13C05, 13C13, 16D70.
DOI: 10.4064/cm114-1-8
Abstract
Let $R$ be the pullback, in the sense of Levy [J. Algebra 71 (1981)], of two local Dedekind domains. We classify all those indecomposable weak multiplication $R$-modules $M$ with finite-dimensional top, that is, such that $M/{\rm Rad} (R) M$ is finite-dimensional over $R/{\rm Rad} (R)$. We also establish a connection between the weak multiplication modules and the pure-injective modules over such domains.
