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Zbl 1111.13008
Aviño-Diaz, Maria A.; Garcia-Puente, Luis D.
Computing the additive structure of indecomposable modules over Dedekind-like rings using Gröbner bases. (English)
[J] J. Algebra Appl. 6, No. 2, 291-304 (2007). ISSN 0219-4988

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 $\Bbb Z \oplus \Bbb Z$.

MSC 2000:: *13C05 Structure of modules (commutative rings)
13E15 Rings and modules of finite generation
13P10 Polynomial ideals, Groebner bases
20C05 Group rings of finite groups and their modules (group theory)

Keywords: Dedekind-like rings; chain modules; finite abelian $p$-groups; Gröbner bases

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