An invariant for modules over a discrete valuation ring
Abstract: Warfield has recently defined a new class of invariants for mixed modules over a discrete valuation ring. These invariants, along with the Ulm invariants, enable Warfield to prove an analogue to Ulm's theorem. Warfield's definition contains two shortcomings. The invariants are defined for a limited class of modules. Moreover it is difficult to show that the invariants are well defined. This paper defines a new invariant which coincides with that of Warfield, and overcomes both difficulties.
Keywords: Discrete valuation ring, module of torsion free rank one, height sequence
Article copyright: © Copyright 1975 American Mathematical Society