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Abelian Groups and Representations of Finite Partially Ordered Sets

Author: David M Arnold
Publisher: New York, NY : Springer New York, 2000.
Series: CMS Books in Mathematics / Ouvrages de mathématiques de la SMC.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
A recurring theme in a traditional introductory graduate algebra course is the existence and consequences of relationships between different algebraic structures. This is also the theme of this book, an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David M Arnold
ISBN: 9781441987501 1441987509
OCLC Number: 853262637
Description: 1 online resource (xii, 244 pages).
Contents: Representations of posets over a field --
Torsion-free Abelian groups --
Butler groups --
Representations over a discrete valuation ring --
Almost completely decomposable groups --
Representations over fields and exact sequences --
Finite rank Butler groups --
Applications of representations and Butler groups.
Series Title: CMS Books in Mathematics / Ouvrages de mathématiques de la SMC.
Responsibility: by David M. Arnold.
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Abstract:

A recurring theme in a traditional introductory graduate algebra course is the existence and consequences of relationships between different algebraic structures. This is also the theme of this book, an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals. His research interests are in abelian group theory and related topics, such as representations of partially ordered sets and modules over discrete valuation rings, subrings of algebraic number fields, and pullback rings. He received his Ph. D. from the University of Illinois, Urbana and was a member of the faculty at New Mexico State University for many years.

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From the reviews: MATHEMATICAL REVIEWS "The book provides a rich source or a variety of readers. As noted above, it offers an excellent and much-needed introduction to the subject of representations Read more...

 
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