Bücher von Eric Jespers

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.

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.