Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This 2004 introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. Various important settings, such as group algebras, Lie algebras, and quantum groups, are sketched at the outset to describe typical problems and provide motivation. The text then develops and illustrates the standard ingredients of the theory: e.g., skew polynomial rings, rings of fractions, bimodules, Krull dimension, linked prime ideals. Recurring emphasis is placed on prime ideals, which play a central role in applications to representation theory. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. Material includes the basic types of quantum groups, which then serve as test cases for the theory developed.

Noetherian rings. --- Noncommutative rings. --- Non-commutative rings --- Associative rings --- Rings, Noetherian --- Commutative rings

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including Nagata, F-finite and excellent rings, Bertini’s Theorem, and Cohen factorizations. Of particular interest is the presentation of Popescu’s Theorem on Neron Desingularization and the structure of regular morphisms, with a complete proof. Classes of Good Noetherian Rings will be an invaluable resource for researchers in commutative algebra, algebraic and arithmetic geometry, and number theory.

Commutative algebra. --- Commutative rings. --- Commutative Rings and Algebras. --- Rings (Algebra) --- Algebra --- Noetherian rings. --- Rings, Noetherian --- Associative rings --- Commutative rings --- Anells noetherians

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic series, and show how these are used in order to present the properties of planar curves. Invariants of non-unique factorizations for numerical semigroups are also studied. These invariants are computationally accessible in this setting, and thus this monograph can be used as an introduction to Factorization Theory. Since factorizations and divisibility are strongly connected, the authors show some applications to AG Codes in the final section. The book will be of value for undergraduate students (especially those at a higher level) and also for researchers wishing to focus on the state of art in numerical semigroups research.

Mathematics. --- Computer science --- Algebraic geometry. --- Commutative algebra. --- Commutative rings. --- Algorithms. --- Combinatorics. --- Algebraic Geometry. --- Commutative Rings and Algebras. --- Discrete Mathematics in Computer Science. --- Noetherian rings. --- Semigroups. --- Ideals (Algebra) --- Algebraic ideals --- Rings, Noetherian --- Algebraic fields --- Rings (Algebra) --- Group theory --- Associative rings --- Commutative rings --- Geometry, algebraic. --- Algebra. --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Combinatorics --- Algebra --- Mathematical analysis --- Algorism --- Arithmetic --- Mathematics --- Algebraic geometry --- Geometry --- Foundations --- Computer science—Mathematics. --- Discrete mathematics. --- Discrete Mathematics. --- Computer mathematics --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis