Noetherian Semigroup Algebras

The ?rst aim of this work is to present the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of certain interesting and important concrete classes of algebras that arise in a variety of areas and have been recently intensively studied. One of the main motivations for this project has been the growing int- est in the class of semigroup algebras (and their deformations) and in the application of semigroup theoretical methods. Two factors seem to be the cause for this. First, this ?eld covers several important classes of algebras that recently arise in a variety of areas. Furthermore, it provides methods to construct a variety of examples and tools to control their structure and properties, that should be of interest to a broad audience in algebra and its applications. Namely, this is a rich resource of constructions not only for the noncommutative ring theorists (and not only restricted to Noetherian rings) but also to researchers in semigroup theory and certain aspects of group theory. Moreover, because of the role of new classes of Noetherian algebras in the algebraic approach in noncommutative geometry, algebras of low dimension (in terms of the homological or the Gelfand-Kirillov - mension) recently gained a lot of attention. Via the applications to the Yang-Baxter equation, the interest also widens into other ?elds, most - tably into mathematical physics.

Offers a comprehensive treatment of the current state of a fast-developing area of noncommutative algebra Provides a significant source of concrete constructions in noncommutative (noetherian) ring theory, semigroup theory and group theory; carefully discusses numerous examples Exhibits strong links between the structure and combinatorics of algebras Explores connections and applications to wider areas of current research, most notably theory of growth of algebras and aspects of mathematical physics

Contenu
Prerequisites on semigroup theory.- Prerequisites on ring theory.- Algebras of submonoids of polycyclic-by-finite groups.- General Noetherian semigroup algebras.- Principal ideal rings.- Maximal orders and Noetherian semigroup algebras.- Monoids of I-type.- Monoids of skew type.- Examples.