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Analytical spaces --- Commutative rings. --- Ideals (Algebra) --- Noetherian rings. --- Sequences (Mathematics) --- Ideals (Algebra). --- Sequences (Mathematics).

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Ordered algebraic structures --- Anneaux neotheriens --- Anneaux non commutatifs --- Neotheriaanse ringen --- Niet-commutatieve ringen --- Noetherian rings --- Noncommutative rings --- 512.55 --- Non-commutative rings --- Associative rings --- Rings, Noetherian --- Commutative rings --- Rings and modules --- 512.55 Rings and modules

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512 --- Noncommutative algebras --- Modules (Algebra) --- Noetherian rings --- Rings, Noetherian --- Associative rings --- Commutative rings --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Algebras, Noncommutative --- Non-commutative algebras --- Noetherian rings. --- Noncommutative algebras. --- Modules (Algebra). --- 512 Algebra --- Algèbres non commutatives --- Algèbres non commutatives.

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A First Course in Noncommutative Rings, an outgrowth of the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson's theory of the radical, representation theory of groups and algebras, prime and semiprime rings, local and semilocal rings, perfect and semiperfect rings, etc. By aiming the level of writing at the novice rather than the connoisseur and by stressing th the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self- study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.

Noetherian rings. --- Noncommutative rings. --- Noncommutative rings --- 512.55 --- 512.55 Rings and modules --- Rings and modules --- Non-commutative rings --- Associative rings --- Ordered algebraic structures --- Algebra. --- Mathematics --- Mathematical analysis

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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)