Extended modules over skew PBW extensions

In the book “Serre’s problem on projective modules” [42], Tsit Yuen Lam defines the class E of extended rings; these rings satisfy the extended version of the Quillen-Suslin theorem. In this thesis we investigate extended modules and rings for skew P BW extensions from a matrix-constructive approach. We determine conditions on the parameters that define a skew extension A = σ(R)hx1, . . . , xni in order to A be projective-free (PF), or more generally, extended (E). Under such particular conditions we prove Vaserstein’s, Quillen’s patching, Horrocks’ and Quillen-Suslin’s theorems for this type of non-commutative rings of polynomial type. Complementary, but as a very important part of the thesis, a computational package has been developed not only for the computations involved in the matrix-constructive proofs related to the PF and E properties, but also for many homological applications of the Gr¨obner theory of skew P BW extensions developed recently in many papers.

• Autores: Fajardo Cardenas, William Alfredo
• Tipo de recurso: Doctoral thesis
• Fecha de publicación: 2019
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/69139
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/69139; http://bdigital.unal.edu.co/70655/
• Palabra clave: 51 Matemáticas / Mathematics; Extended modules; Extended rings; Skew P BW extensions; Bass-Quillen conjecture; Quillen-Suslin theorem; Matrix-constructive; algorithmic proofs; Gröbner basis; Skew P BW extensions; Módulos extendidos; Anillos extendidos; Extensiones P BW torcidas; Conjetura de Bass-Quillen; Teorema de Quillen-Suslin; Aproximación matricial constructiva; Pruebas algorítmicas; Bases de Gröbner; Extensiones P BW torcidas
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional