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## Details

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. |

More information: |

### 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.

## Reviews

*Editorial reviews*

Publisher Synopsis

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 of posets. It could readily be used for a second year graduate course in algebra, with many tools and suggestions for cutting edge research. Finally, it is a handy reference for anyone interested in the study of torsion-free abelian groups of finite rank or related questions in representations of posets. If writing this review had not put a free copy on my bookshelf, I would rush to the web to order one." Read more...

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