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An iterative construction of bases for finitely generated modules over principal ideal domains. (English) Zbl 0812.13007

The authors give a new proof for the existence of a basis of a finitely generated module \(V\) over a principal ideal ring; this proof is simpler and more lucid than those known in the literature and remains valid whether \(V\) does or does not have elements of infinite order.

MSC:

13C05 Structure, classification theorems for modules and ideals in commutative rings
13F30 Valuation rings
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References:

[1] Abian, A.: Construction of a basis for finitely generated Abelian groups. Abstracts, Amer. Math. Soc. 12 (1991), 507.
[2] Hungerford, T. W.: Algebra. Springer-Verlag, New York, 1974. · Zbl 0293.12001
[3] Jacobson, N.: Lectures in Abstract Algebra. Springer-Verlag, New York, 1951. · Zbl 0044.26002
[4] Shenkman, E.: The basis theorem for finitely generated Abelian groups. American Mathematical Monthly 67 (1960), 770. · Zbl 0102.26703
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