ABSTRACT

Gathers and unifies the results of the theory of noncommutative semigroup rings, primarily drawing on the literature of the last 10 years, and including several new results. Okninski (Warsaw U., Poland) restricts coverage to the ring theoretical properties for which a systematic treatment is current

part I|78 pages

Semigroups and Their Algebras

chapter 1|10 pages

Completely 0-Simple and Linear Semigroups

chapter 2|8 pages

Semigroups with Finiteness Conditions

chapter 3|12 pages

Weakly Periodic Semigroups

chapter 4|14 pages

Semigroup Algebras

General Results and Techniques

chapter 5|18 pages

Munn Algebras

chapter 6|14 pages

Gradations

part II|60 pages

Semigroup Algebras of Cancellative Semigroups

chapter 7|14 pages

Groups of Fractions

chapter 8|12 pages

Semigroups of Polynomial Growth

chapter 9|12 pages

Δ-Methods

chapter 10|10 pages

Unique-/Two-Unique-Product Semigroups

chapter 11|10 pages

Subsemigroups of Polycyclic-by-Finite Groups

part III|74 pages

Finiteness Conditions

chapter 12|12 pages

Noetherian Semigroup Algebras

chapter 13|6 pages

Spectral Properties

chapter 14|20 pages

Descending Chain Conditions

chapter 15|8 pages

Regular Algebras

chapter 16|18 pages

Self-lnjectivity

chapter 17|8 pages

Other Finiteness Conditions: A Survey

part IV|114 pages

Semigroup Algebras Satisfying Polynomial Identities

chapter 18|6 pages

Preliminaries on PI-Algebras

chapter 19|18 pages

Semigroups Satisfying Permutational Property

chapter 20|16 pages

PI-Semigroup Algebras

chapter 21|12 pages

The Radical

chapter 22|8 pages

Prime PI-Algebras

chapter 23|18 pages

Dimensions

chapter 24|20 pages

Monomial Algebras

chapter 25|14 pages

Azumaya Algebras

part V|8 pages

Problems