Algebra and Applications

Noetherian Semigroup Algebras

Authors: Jespers, Eric, Okninski, Jan

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About this book

Within the last decade, semigroup theoretical methods have occurred naturally in many aspects of ring theory, algebraic combinatorics, representation theory and their applications. In particular, motivated by noncommutative geometry and the theory of quantum groups, there is a growing interest in the class of semigroup algebras and their deformations.

This work presents a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of important classes of algebras that arise in a variety of areas and have been recently intensively studied. Several concrete constructions are described in full detail, in particular intriguing classes of quadratic algebras and algebras related to group rings of polycyclic-by-finite groups. These give new classes of Noetherian algebras of small Gelfand-Kirillov dimension. The focus is on the interplay between their combinatorics and the algebraic structure. This yields a rich resource of examples that are of interest not only for the noncommutative ring theorists, but also for researchers in semigroup theory and certain aspects of group and group ring theory. Mathematical physicists will find this work of interest owing to the attention given to applications to the Yang-Baxter equation.

Reviews

From the reviews:

"This book presents the main results and methods of the theory of Noetherian semigroup algebras over fields. … This is a highly technical and specialized monograph that will primarily be of use to researchers in the theory of semigroup algebras … . The many examples given in detail, and the general theory developed, may prove useful to those working in ring or semigroup theory." (Henry E. Heatherly, Mathematical Reviews, Issue 2007 k)

"This work presents a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. … The main subject in this book is to present when some semigroup algebras are Noetherian and how they are under the Noetherian condition. … This book is a good reference for researchers who are interested in non-commutative algebra and non-commutative geometry through the method of semigroups." (Li Fang, Zentralblatt MATH, Vol. 1135 (13), 2008)

"The book under review is testament to the huge amount and the depth of research on Noetherian semigroup algebras. … The authors have brought together work from a significant number of research papers and made a coherent whole. … it is definitely the place to learn about Noetherian semigroup algebras. Essential reading for people interested in semigroup algebras, it will also be of interest to semigroup theorists, particularly because of the wealth of new examples of semigroups it provides." (John Fountain, Semigroup Forum, Vol. 79, 2009)


Table of contents (10 chapters)

Table of contents (10 chapters)
  • Introduction

    Pages 1-5

    Jespers, Eric (et al.)

  • Prerequisites on semigroup theory

    Pages 7-35

    Jespers, Eric (et al.)

  • Prerequisites on ring theory

    Pages 37-61

    Jespers, Eric (et al.)

  • Algebras of submonoids of polycyclic-by-finite groups

    Pages 63-115

    Jespers, Eric (et al.)

  • General Noetherian semigroup algebras

    Pages 117-147

    Jespers, Eric (et al.)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-1-4020-5810-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-1-4020-5809-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $119.00
price for USA in USD
  • ISBN 978-90-481-7448-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Noetherian Semigroup Algebras
Authors
Series Title
Algebra and Applications
Series Volume
7
Copyright
2007
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-5810-3
DOI
10.1007/1-4020-5810-1
Hardcover ISBN
978-1-4020-5809-7
Softcover ISBN
978-90-481-7448-5
Series ISSN
1572-5553
Edition Number
1
Number of Pages
X, 364
Topics