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 Title Computing the additive structure of indecomposable modules over Dedekind-like rings using Gr\"obner bases. Author(s) Maria Alicia Avino, Luis David Garcia-Puente Type Article in Journal Abstract We introduce a general constructive method to find a $p$-basis (and the Ulm invariants) of a finite Abelian $p$-group $M$. This algorithm is based on Gr\"obner bases theory. We apply this method to determine the additive structure of indecomposable modules over the following Dedeking-like rings: $\Z C_p$, where $C_p$ is the cyclic group of order a prime $p$, and the $p-$pullback $\{\Z \rightarrow \Z_p \leftarrow \Z \}$ of $\Z \oplus \Z$. Keywords Dedekind-like rings, chain modules, finite Abelian $p$-groups, Gr\"obner bases. Length 12 File URL http://arxiv.org/abs/math.AC/0603304 Language English Year 2006 Note submitted for publication Edition 0 Translation No Refereed Yes How published submitted Organization Texas A&M University
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