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...

Table of Contents:

• Part 1 :Finitely Generated Abelian Groups: Matrices with Integer Entries: The Smith Normal Form
• Basic Theory of Additive Abelian Groups
• Decomposition of Finitely Generated  Z-Modules. Part 2: Similarity of Square Matrices over a Field: The Polynomial Ring F[x] and Matrices over F[x]- F[x] Modules: Similarity of t xt Matrices over a Field F
• Canonical Forms and Similarity Classes of Square Matrices over a Field.        .