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.


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