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Quasi-basic submodules over valuation domains. (English) Zbl 0790.13002

The authors define two kinds of new invariants for modules over valuation domains. The first ones form a complete independent set of invariants for direct sums of uniserial modules, including the non-standard ones, and are related to maximal pure direct sums of uniserial submodules isomorphic to a fixed uniserial module. - The second kind of invariants are related to maximal pure direct sums of arbitrary uniserial submodules.

MSC:

13C05 Structure, classification theorems for modules and ideals in commutative rings
13F30 Valuation rings
13C13 Other special types of modules and ideals in commutative rings
13A50 Actions of groups on commutative rings; invariant theory
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References:

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