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The free rank of a finitely generated module over a PID
Definition
Let be a finitely generated module over a principal ideal domain . Its free rank, denoted , is the unique integer for which its invariant-factor decomposition has free summand .
Uniqueness follows from Uniqueness of invariant factors and elementary divisors over a PID and agrees with the rank convention for finite free modules in Invariant basis number and the rank of a free module. In particular a torsion module has free rank .
Depends on
Used by
Dependency tree · two levels
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Sources
- K. Conrad, Modules over a PID, Sections 4-5 (standard reference, not scraped)
- M. Brussel, Finitely Generated Modules over a PID, Sections 3-5 (standard reference, not scraped)