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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.
MSC:
13F30 Valuation rings
13C13 Other special types of modules and ideals in commutative rings
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References:
[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
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