zbMATH — the first resource for mathematics

Hulls of mixed modules with finite quotient \(p\)-rank. (English) Zbl 0953.13010
The structure of mixed modules over a discrete valuation domain \(R\) with a prime \(p\) is investigated. After a short introduction the torsion modules are characterized in terms of free representations in the second part. In the next one a general representation of mixed module is given and in the last item the notion of the hull of a mixed module is introduced and the isomorphism classes of mixed modules with finite \(p\)-ranks (the dimension of \(G/pG\) over the field \(R/pR\)) are described by using the automorphisms of the hull.
13F30 Valuation rings
13C13 Other special types of modules and ideals in commutative rings
Full Text: DOI EuDML
[1] K. Benabdallah and K. Honda: Straight bases of abelian \(p\)-groups. Abelian Group Theory, Proceedings, Honolulu (1982/83), Lecture Notes 1006, pp. 556-561.
[2] L. Fuchs: Infinite Abelian Groups I+II. Academic Press, 1970, 1973. · Zbl 0209.05503
[3] O. Mutzbauer and E. Toubassi: A splitting criterion for a class of mixed modules. Rocky Mountain J. Math. 24 (1994), 1533-1543. · Zbl 0836.13004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.