Noncommutative polynomial algebras of solvable type and their modules : basic constructive-computational theory and methods /: basic constructive-computational theory and methods. (2021)

• Record Type: Book
• Further Information: Note: Huishi Li.
• Authors: Li, Huishi
• Contents: 1. Solvable Polynomial Algebras. 1.1. Definition, Examples, Basic Properties. 1.2. A Constructive Characterization. 1.3. The Solvable Polynomial Algebras H(A). 1.4. Gröbner Bases of Left Ideals. 1.5. Finite Gröbner Bases → The Noetherianess. 1.6. Elimination in Left Ideals. 2. Gröbner Basis Theory of Free Modules. 2.1. Monomial Orderings on Free Modules. 2.2. Gröbner Bases of Submodules. 2.3. The Noncommutative Buchberger Algorithm. 2.4. Elimination in Submodules. 2.5. Application to Module Homomorphisms. 3. Computation of Finite Free Resolutions and Projective Dimension. 3.1. Computation of Syzygies. 3.2. Computation of Finite Free Resolutions. 3.3. Global Dimension and Stability. 3.4. Computation of p.dimA M. 4. Computation of Minimal Finite Graded Free Resolutions. 4.1. N-graded Solvable Polynomial Algebras of (B; d( ))-type. 4.2. N-Graded Free Modules. 4.3. Computation of Minimal Homogeneous Generating Sets. 5. Computation of Minimal Finite Filtered Free Resolutions. 5.1. N-Filtered Solvable Polynomial Algebras of (B; d( ))-Type. 5.2. N-Filtered Free Modules. 5.3. Filtered-Graded Transfer of Gröbner Bases for Modules. 5.4. F-Bases and Standard Bases with Respect to Good Filtration. 5.5. Computation of Minimal F-Bases and Minimal Standard Bases. 5.6. Minimal Filtered Free Resolutions and Their Uniqueness. 5.7. Computation of Minimal Finite Filtered Free Resolutions. Appendix.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2021
• Extent: 1 online resource
• Subjects: 512.48; Noncommutative algebras; PI-algebras; Solvable groups; Computable functions; Modules (Algebra); Free resolutions (Algebra)
• Languages: English
• ISBNs: 9781000471120; 9781000471106; 9781003213192
• Related ISBNs: 9781032079882
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
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