عنوان

Algorithmic methods in non-commutative algebra :

شابک

9048163285

شابک

9401702853

شابک

9789048163281

شابک

9789401702850

شماره

b596552

عنوان اصلي

Algorithmic methods in non-commutative algebra :

نام عام مواد

[Book]

ساير اطلاعات عنواني

applications to quantum groups

نام نخستين پديدآور

by José L. Bueso, José Gomez-Torrecillas, Alain Verschoren.

محل نشرو پخش و غیره

Dordrecht ; London

نام ناشر، پخش کننده و غيره

Springer

تاریخ نشرو بخش و غیره

2011

نام خاص و کميت اثر

(1 v).

عنوان فروست

Mathematical modelling. Theory and applications, v. 17

متن يادداشت

Originally published: 2003.

متن يادداشت

Introduction. 1: Generalities on rings. 1. Rings and ideals. 2. Modules and chain conditions. 3. Ore extensions. 4. Factorization. 5. Other examples. 6. Quantum groups. 2: Groebner basis computation algorithms. 1. Admissible orders. 2. Left Poincare-Birkhoff-Witt Rings. 3. Examples. 4. The Division Algorithm. 5. Groebner bases for left ideals. 6. Buchberger's Algorithm. 7. Reduced Groebner Bases. 8. Poincare-Birkhoff-Witt rings. 9. Effective computations for two-sided ideals. 3: Poincare-Birkhoff-Witt Algebras. 1. Bounding quantum relations. 2. Misordering. 3. The Diamond Lemma. 4. Poincare-Birkhoff-Witt Theorems. 5. Examples. 6. Iterated Ore Extensions. 4: First applications. 1. Applications to left ideals. 2. Cyclic finite-dimensional modules. 3. Elimination. 4. Graded and filtered algebras. 5. The omega-filtration of a PBW algebra. 6. Homogeneous Groebner bases. 7. Homogenization. 5: Groebner bases for modules. 1. Groebner bases and syzygies. 2. Computation of the syzygy module. 3. Admissible orders in stable subsets. 4. Groebner bases for modules. 5. Groebner bases for subbimodules. 6. Elementary applications of Groebner bases for modules. 7. Graded and filtered modules. 8. The omega-filtration of a module. 9. Homogeneous Groebner bases. 10. Homogenization. 6:Syzygies and applications. 1. Syzygies for modules. 2. Intersections. 3. Applications to finitely presented modules. 4. Schreyer's order. 5. Free resolutions. 6. Computation of Hom and Ext. 7: The Gelfand-Kirillov dimension and the Hilbert polynomial. 1. The Gelfand-Kirillov dimension. 2. The Hilbert function of a stable subset. 3.The Hilbert function of a module over a PBW algebra. 4. The Gelfand-Kirillov dimension of PBW algebras. 8: Primality. 1. Localization. 2. The Ore condition and syzygies. 3. A primality test. 4. The primality test in iterated differential operator rings. 5. The primality test in coordinate rings of quantum spaces. Index. References.

موضوع مستند نشده

Algorithms.

موضوع مستند نشده

Noncommutative algebras.

موضوع مستند نشده

Quantum groups.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by José L. Bueso, José Gomez-Torrecillas, Alain Verschoren.

مستند نام اشخاص تاييد نشده

A Verschoren

مستند نام اشخاص تاييد نشده

José Gómez-Torrecillas

مستند نام اشخاص تاييد نشده

José Luis Bueso

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y