COMPUTING THE ADDITIVE STRUCTURE OF INDECOMPOSABLE MODULES OVER DEDEKIND-LIKE RINGS USING GRÖBNER BASES

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.