Description 
1 online resource (ix, 361 pages) 
Series 
Algebra and applications ; v. 7 

Algebras and applications ; v. 7.

Contents 
Introduction; Prerequisites on semigroup theory; Prerequisites on ring theory; Algebras of submonoids of polycyclicbyfinite groups; General Noetherian semigroup algebras; Principal ideal rings; Maximal orders and Noetherian semigroup algebras; Monoids of Itype; Monoids of skew type; Examples 
Summary 
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 polycyclicbyfinite groups. These give new classes of Noetherian algebras of small GelfandKirillov 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 YangBaxter equation 
Bibliography 
Includes bibliographical references and index 
Notes 
English 

Print version record 
In 
Springer ebooks 
Subject 
Semigroup algebras.


Noetherian rings.


Noetherian rings.


Semigroup algebras.

Form 
Electronic book

Author 
Okniński, Jan, 1954

ISBN 
9781402058103 

1402058101 

9781402058097 

1402058098 

9048174481 

9789048174485 
