Calculating indicators in a class of mixed modules. (English) Zbl 0883.13010
Arnold, David M. (ed.) et al., Abelian groups and modules. Proceedings of the international conference at Colorado Springs, CO, USA, August 7–12, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 182, 291-301 (1996).
The authors study indicators of a class \(H\) of mixed modules over a discrete valuation ring with the property that the torsion submodule is a direct sum of cyclics and the quotient modulo torsion is divisible of arbitrary rank. They do this by using relation systems of modules in \(H\). They further restrict their study to the subclass \(H'\) of \(H\) consisting of modules of torsion-free rank 1.
In section 4, they derive equivalent conditions
(i) for a module \(G\) in \(H'\) with relation system to have an indicator of \(\infty\)-type
(ii) for a reduced module \(G\) in \(H'\) with relation system to have an indicator of finite type or \(w\)-type.
In the final section, the authors study the structure of modules in the class \(H\) of fixed torsion type \(\lambda\).
For the entire collection see [Zbl 0853.00035].
In section 4, they derive equivalent conditions
(i) for a module \(G\) in \(H'\) with relation system to have an indicator of \(\infty\)-type
(ii) for a reduced module \(G\) in \(H'\) with relation system to have an indicator of finite type or \(w\)-type.
In the final section, the authors study the structure of modules in the class \(H\) of fixed torsion type \(\lambda\).
For the entire collection see [Zbl 0853.00035].
Reviewer: V.A.Hiremath (Dharwad)
