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Presents the English translation of Kaljulaid's 1979 Tartu/Minsk Candidate thesis. The thesis was devoted to representation theory in the spirit of his thesis advisor BI Plotkin. Through representation theory, Kaljulaid became also interested in automata theory, which at a later phase became his main area of interest.

Semigroups. --- Semigroup algebras. --- Machine theory. --- Mathematics --- Math --- Science --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Logic, Symbolic and mathematical --- Recursive functions --- Robotics --- Algebras, Semigroup --- Algebra --- Group theory --- History.

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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.

Noetherian rings. --- Semigroup algebras. --- Algebras, Semigroup --- Algebra --- Rings, Noetherian --- Associative rings --- Commutative rings --- Group theory. --- Algebra. --- Group Theory and Generalizations. --- Associative Rings and Algebras. --- Mathematics --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Associative rings. --- Rings (Algebra). --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra)

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Several of the contributions to this volume bring forward many mutually beneficial interactions and connections between the three domains of the title. Developing them was the main purpose of the NATO ASI summerschool held in Montreal in 2003. Although some connections, for example between semigroups and automata, were known for a long time, developing them and surveying them in one volume is novel and hopefully stimulating for the future. Another aspect is the emphasis on the structural theory of automata that studies ways to construct big automata from small ones. The volume also has contributions on top current research or surveys in the three domains. One contribution even links clones of universal algebra with the computational complexity of computer science. Three contributions introduce the reader to research in the former East block.

Abstract automata --- Abstract machines --- Algebra [Multiple ] --- Algebra [Universal ] --- Algebra [Universele ] --- Algèbre universelle --- Automata --- Automates [Théorie des ] --- Automates mathématiques [Théorie des ] --- Machine theory --- Machines [Théorie des ] --- Mathematical machine theory --- N-way algebra --- Semigroup algebras --- Théorie des automates mathématiques --- Théorie des machines --- Universal algebra --- Universele algebra --- Wiskundige automaten [Theorie van de ] --- Algebra, Universal. --- Semigroup algebras. --- Machine theory. --- Algèbres de semi-groupes --- Automates mathématiques, Théorie des --- Algebra, Universal --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Algèbre universelle --- Algèbres de semi-groupes --- Automates mathématiques, Théorie des --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Algebras, Semigroup --- Algebra, Multiple --- Multiple algebra --- Mathematics. --- Algebra. --- Group theory. --- General Algebraic Systems. --- Group Theory and Generalizations. --- Algorithms --- Logic, Symbolic and mathematical --- Recursive functions --- Robotics --- Algebra, Abstract --- Numbers, Complex --- Groups, Theory of --- Substitutions (Mathematics) --- Mathematical analysis --- Structural theory