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Similarity of integer matrices / David Husert. Paderborn, 2017
Inhalt
Introduction
I Semisimple Matrices
Module-Theoretic Approach I
Full Modules over Orders
The Theorem of Latimer and MacDuffee
Equivalence over Maximal Orders
Matrix Orders
Units of Matrix Orders
The Conductor
Some Remarks on the Number of Module Classes
Algorithms
Localizations of Orders
Basic Properties
Decomposition of Quotient Rings
Characterization of Units
Making Ideals Coprime to the Conductor
Algorithms
Principal Ideal Testing
The Commutative Case
The Noncommutative Case
Algorithms
II Nilpotent Matrices
Module-Theoretic Approach II
Nilpotent Matrices over Orders
Similarity of Free Modules
Enumerating Free Modules of Minimal Index
Nilpotent Integer Matrices
Algorithms
Examples and Running Times
Final Remarks
Bibliography
List of Symbols
Index
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