this is an account of how a certain fundamental algebraic concept can be introduced, developed, and applied to solve some concrete algebraic problems. The book is divided into three parts. The first is concerned with defining concepts and terminology, assembling elementary facts, and developing the theory of factorization in a principal ideal domain. The second part deals with the main decomposition theorems which describe the structure of finitely generated modules over a principal ideal domain. The third part contains the applications of these theorems. This book may be of interest to undergraduates taking courses in algebra.
Sprache
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Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
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ISBN-13
978-0-412-09810-9 (9780412098109)
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Schweitzer Klassifikation
Part I: rings and modules; rings - definitions and examples; subrings, homomorphisms and ideals; construction of new rings; factorization in integral domains; modules; some special classes of modules. Part II: direct decomposition of a finitely-generated module over a principal ideal domain; submodules of free modules; decomposition theorems; decomposition theorems - a matrix-free approach. Part III: applications to groups and matrices; finitely-generated abelian groups; linear transformations, matrices and canonical forms; computation of canonical forms.
