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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: C p , where C p is the cyclic group of order a prime p, and the p-pullback { p } of .
MSC:
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)