Modules over a principal ideal domain

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Thomas Leo Stowell (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Advisor
Kenneth Byrd

Abstract: This thesis determines the structure of certain modules over a principal ideal domain, namely the divisible modules and the finitely generated modules. The author proves that any divisible module M over a principal ideal domain D is isomorphic to a direct sum of modules each of which is a copy of the quotient field KD or to Dp" for various primes p ? D. The author also proves that a finitely generated module is isomorphic to a finite product of cyclic modules. Any finitely generated module is characterized up to isomorphism by certain algebraic invariants. The results on finitely generated modules are then applied to vector space theory to develop the rational and Jordan canonical forms.

Additional Information

Publication
Thesis
Language: English
Date: 1974
Subjects
Modules (Algebra)
Isomorphisms (Mathematics)
Vector spaces

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