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Computing the additive structure of indecomposable modules over Dedekind-like rings using Gröbner bases. (English) Zbl 1111.13008
Summary: 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 Gröbner bases theory. We apply this method to determine the additive structure of indecomposable modules over the following Dedeking-like rings: $\Bbb ZC_{p}$, where $C_{p}$ is the cyclic group of order a prime $p$, and the $p$-pullback $\{\Bbb Z \rightarrow \Bbb Z_{p} \leftarrow \Bbb Z\}$ of $\Bbb Z \oplus \Bbb Z$.
13C05Structure of modules (commutative rings)
13E15Rings and modules of finite generation
13P10Gröbner bases; other bases for ideals and modules
20C05Group rings of finite groups and their modules (group theory)
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