Twisted Blanchfield pairings and twisted signatures I: Algebraic background

This is the first paper in a series of three devoted to studying twisted linking forms of knots and three-manifolds. Its function is to provide the algebraic foundations for the next two papers by describing how to define and calculate signature invariants associated to a linking form M x M -> F(t)/F [t +/- 1] for F = R, C, where M is a torsion F [t +/- 1]-module. Along the way, we classify such linking forms up to isometry and Witt equivalence and study whether they can be represented by matrices. (c) 2022 Elsevier Inc. All rights reserved.