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Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra
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Doelstelling: Op conferenties gebeurt het soms dat de tolk de spreker niet goed kan zien. In deze scriptie wordt aan de hand van een vergelijkende studie nagegaan wat het belang van nonverbale communicatie is, voor de semantische/pragmatische output van een tolkprestatie. Middelen of methode: Met een periode van twee maanden tussen de vertolkingen werd een tekst die in het Engels gesproken werd, twee keer getolkt naar het Nederlands door één en dezelfde tolk. De eerste keer kon de tolk de spreker niet zien, de tweede keer wel. De verschillen tussen de prestaties en de brontekst werden ingedeeld in: toevoegingen (nieuwe informatie, explicitering, voegwoorden), weglatingen (verdwenen informatie, implicitering, voegwoorden), veranderingen (voegwoorden, andere) en herhalingen (inclusief versprekingen en aarzelingen). Beide vertolkingen werden aan deze indeling getoetst en daarna met elkaar vergeleken. Resultaten: Uit de analyse bleek dat de tweede vertolking semantisch beter aansloot bij de brontekst dan de eerste: er werd minder informatie weggelaten, toegevoegd of veranderd. Ook werden er minder versprekingen, herhalingen en aarzelingen gemaakt. Zicht hebben van de spreker had daarentegen weinig of geen invloed op het gebruikte aantal impliciteringen en expliciteringen en het gebruik van voegwoorden.
Additions. --- Coherence. --- Hesitations. --- Nonverbal communication. --- Omissions. --- Pragmatics. --- Repetitions. --- Semantics. --- Simultaneous interpreting. --- Substitutions. --- Tolkstudie.
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After a forty-year lull, the study of word-values in groups has sprung back into life with some spectacular new results in finite group theory. These are largely motivated by applications to profinite groups, including the solution of an old problem of Serre. This book presents a comprehensive account of the known results, both old and new. The more elementary methods are developed from scratch, leading to self-contained proofs and improvements of some classic results about infinite soluble groups. This is followed by a detailed introduction to more advanced topics in finite group theory, and a full account of the applications to profinite groups. The author presents proofs of some very recent results and discusses open questions for further research. This self-contained account is accessible to research students, but will interest all research workers in group theory.
Finite groups. --- Profinite groups. --- Solvable groups. --- Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Soluble groups --- Group theory --- Groups, Finite --- Modules (Algebra)
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The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed, first of all, to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but should also prove useful to tutors and researchers.
Semigroups. --- Semigroups --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Mathematics. --- Combinatorics. --- Group Theory and Generalizations. --- Group theory --- Combinatorics --- Mathematical analysis
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A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series, which consists of the subgroups determined by the augmentation powers, is a challenging task. This monograph presents an exposition of different methods for investigating this relationship. In addition to group theorists, the results are also of interest to topologists and number theorists. The approach is mainly combinatorial and homological. A novel feature is an exposition of simplicial methods for the study of problems in group theory.
Algebraic topology --- algebra --- topologie (wiskunde) --- Category theory. Homological algebra --- Algebra --- wiskunde --- Group theory --- Algebra, Homological --- 512.54 --- Groups, Theory of --- Substitutions (Mathematics) --- Homological algebra --- Algebra, Abstract --- Homology theory --- 512.54 Groups. Group theory --- Groups. Group theory
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The definition of Rouquier for the families of characters introduced by Lusztig for Weyl groups in terms of blocks of the Hecke algebras has made possible the generalization of this notion to the case of complex reflection groups. The aim of this book is to study the blocks and to determine the families of characters for all cyclotomic Hecke algebras associated to complex reflection groups. This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory, and can also serve as an introduction to the Hecke algebras of complex reflection groups.
Hecke algebras --- Representations of groups --- Cyclotomy --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Algebra --- Cyclotomy. --- Hecke algebras. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Algebras, Hecke --- Equations, Cyclotomic --- Mathematics. --- Group theory. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Math --- Science --- Group algebras --- Number theory --- Equations, Abelian --- Group theory
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Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ([33], [34], [9]). A continuous geometry is an indecomposable, continuous, complemented modular lattice that is not ?nite-dimensional ([8, page 155], [32, page V]). Von Neumann proved ([32, Theorem 14. 1, page 208], [8, page 162]): Every continuous geometry is isomorphic to the lattice of right ideals of some regular ring. The book of K. R. Goodearl ([14]) gives an extensive account of various types of regular rings and there exist several papers studying modules over regular rings ([27], [31], [15]). In abelian group theory the interest lay in determining those groups whose endomorphism rings were regular or had related properties ([11, Section 112], [29], [30], [12], [13], [24]). An interesting feature was introduced by Brown and McCoy ([4]) who showed that every ring contains a unique largest ideal, all of whose elements are regular elements of the ring. In all these studies it was clear that regularity was intimately related to direct sum decompositions. Ware and Zelmanowitz ([35], [37]) de?ned regularity in modules and studied the structure of regular modules. Nicholson ([26]) generalized the notion and theory of regular modules. In this purely algebraic monograph we study a generalization of regularity to the homomorphism group of two modules which was introduced by the ?rst author ([19]). Little background is needed and the text is accessible to students with an exposure to standard modern algebra. In the following, Risaringwith1,and A, M are right unital R-modules.
Endomorphism rings. --- Homomorphisms (Mathematics). --- Modules (Algebra). --- Rings (Algebra). --- Modules (Algebra) --- Homomorphisms (Mathematics) --- Rings (Algebra) --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Algebraic rings --- Ring theory --- Finite number systems --- Modular systems (Algebra) --- Mathematics. --- Algebra. --- Associative rings. --- Group theory. --- Associative Rings and Algebras. --- Group Theory and Generalizations. --- Algebraic fields --- Functions --- Finite groups --- Groups, Theory of --- Substitutions (Mathematics) --- Mathematical analysis
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A Course on Finite Groups introduces the fundamentals of group theory to advanced undergraduate and beginning graduate students. Based on a series of lecture courses developed by the author over many years, the book starts with the basic definitions and examples and develops the theory to the point where a number of classic theorems can be proved. The topics covered include: group constructions; homomorphisms and isomorphisms; actions; Sylow theory; products and Abelian groups; series; nilpotent and soluble groups; and an introduction to the classification of the finite simple groups. A number of groups are described in detail and the reader is encouraged to work with one of the many computer algebra packages available to construct and experience "actual" groups for themselves in order to develop a deeper understanding of the theory and the significance of the theorems. Numerous problems, of varying levels of difficulty, help to test understanding. A brief resumé of the basic set theory and number theory required for the text is provided in an appendix, and a wealth of extra resources is available online at www.springer.com, including: hints and/or full solutions to all of the exercises; extension material for many of the chapters, covering more challenging topics and results for further study; and two additional chapters providing an introduction to group representation theory.
Electronic books. -- local. --- Finite groups. --- Mathematics. --- Finite groups --- Mathematics --- Algebra --- Physical Sciences & Mathematics --- Math --- Groups, Finite --- Algebra. --- Group theory. --- Science education. --- Science Education. --- Group Theory and Generalizations. --- Science --- Science education --- Scientific education --- Groups, Theory of --- Substitutions (Mathematics) --- Mathematical analysis --- Group theory --- Modules (Algebra) --- Study and teaching.
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The book discusses classical Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it discusses algebraic closure and infinite Galois extensions, and concludes with a new chapter on transcendental extensions. Key topics and features of this second edition: - Approaches Galois theory from the linear algebra point of view, following Artin; - Presents a number of applications of Galois theory, including symmetric functions, finite fields, cyclotomic fields, algebraic number fields, solvability of equations by radicals, and the impossibility of solution of the three geometric problems of Greek antiquity. Review from the first edition: "The text offers the standard material of classical field theory and Galois theory, though in a remarkably original, unconventional and comprehensive manner … . the book under review must be seen as a highly welcome and valuable complement to existing textbook literature … . It comes with its own features and advantages … it surely is a perfect introduction to this evergreen subject. The numerous explaining remarks, hints, examples and applications are particularly commendable … just as the outstanding clarity and fullness of the text." (Zentralblatt MATH, Vol. 1089 (15), 2006) Steven H. Weintraub is a Professor of Mathematics at Lehigh University and the author of seven books. This book grew out of a graduate course he taught at Lehigh. He is also the author of Algebra: An Approach via Module Theory (with W. A. Adkins).
Galois theory. --- Galois theory --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematics. --- Algebra. --- Field theory (Physics). --- Group theory. --- Number theory. --- Field Theory and Polynomials. --- Group Theory and Generalizations. --- Number Theory. --- Number study --- Numbers, Theory of --- Groups, Theory of --- Substitutions (Mathematics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematical analysis --- Math --- Science --- Equations, Theory of --- Group theory --- Number theory --- Field theory (Physics)
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This monograph is the first devoted exclusively to the development of the theory of numerical semigroups. In this concise, self-contained text, graduate students and researchers will benefit from this broad exposition of the topic. Key features of "Numerical Semigroups" include: - Content ranging from the basics to open research problems and the latest advances in the field; - Exercises at the end of each chapter that expand upon and support the material; - Emphasis on the computational aspects of the theory; algorithms are presented to provide effective calculations; - Many examples that illustrate the concepts and algorithms; - Presentation of various connections between numerical semigroups and number theory, coding theory, algebraic geometry, linear programming, and commutative algebra would be of significant interest to researchers. "Numerical Semigroups" is accessible to first year graduate students, with only a basic knowledge of algebra required, giving the full background needed for readers not familiar with the topic. Researchers will find the tools presented useful in producing examples and counterexamples in other fields such as algebraic geometry, number theory, and linear programming.
Ideals (Algebra). --- Semigroups. --- Semigroups --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Mathematics. --- Algebra. --- Ordered algebraic structures. --- Number theory. --- Group Theory and Generalizations. --- Number Theory. --- General Algebraic Systems. --- Order, Lattices, Ordered Algebraic Structures. --- Group theory --- Number study --- Numbers, Theory of --- Mathematical analysis --- Algebraic structures, Ordered --- Structures, Ordered algebraic
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