Noncommutative Polynomial Algebras of Solvable Type and Their Modules

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. Groebner Bases of Left Ideals. 1.5. Finite Groebner Bases ? The Noetherianess. 1.6. Elimination in Left Ideals. 2. Groebner Basis Theory of Free Modules. 2.1. Monomial Orderings on Free Modules. 2.2. Groebner 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.dimAM. 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 Groebner 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.