Computing the Additive Structure of Indecomposable Modules Over Dedekind-Like Rings Using Gröbner Bases

Abstract

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 Gröbner bases theory. We apply this method to determine the additive structure of indecomposable modules over the following Dedeking-like rings: ZCp, where Cp is the cyclic group of order a prime p, and the p−pullback {Z → Zp ← Z} of Z ⊕ Z.