Abstract

By PFM, we mean a finitely generated module over a principal ideal domain; a linear sentence is a sentence that contains no disjunctive and negative symbols. In this paper, we present an algorithm which decides the truth for linear sentences on a given PFM, and we discuss its time complexity. In particular, when the principal ideal domain is the ring of integers or a univariate polynomial ring over the field of rationals, the algorithm is polynomial-time. Finally, we consider some applications to Abelian groups