Abstract
Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincare- Birkhoff Witt) extensions. In the present paper we study two aspects of these non-commutative rings: their finitely generated projective modules from a matrix-constructive approach, and the construction of the Gröbner theory for their left ideals and modules. These two topics have interesting applications in functional linear systems and in non-commutative geometry.
| Original language | English |
|---|---|
| Pages (from-to) | 1-50 |
| Number of pages | 50 |
| Journal | Dissertationes Mathematicae |
| Volume | 521 |
| DOIs | |
| State | Published - 2017 |
| Externally published | Yes |
Keywords
- Buchberger’s algorithm
- Hermite rings
- Matrix-constructive methods
- Non-commutative Gröbner bases
- Projective modules
- Skew PBW extensions
- Stable rank
- Stably free modules