Finitely Generated Abelian Groups and Similarity of Matrices over a Field

• Main Author: Norman, Christopher (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2012.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Algebra.; Field theory (Physics).; Group theory.; Matrix theory.; Algorithms.; Field Theory and Polynomials.; Group Theory and Generalizations.; Linear and Multilinear Algebras, Matrix Theory.

At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common.  However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both...