Název:
Serreho hypotéza o projektivních modulech nad okruhy polynomů
Překlad názvu:
Serre's conjecture on projective modules over polynomial rings
Autoři:
Young, Edward ; Shaul, Liran (vedoucí práce) ; Bird, Isaac (oponent) Typ dokumentu: Bakalářské práce
Rok:
2023
Jazyk:
eng
Abstrakt: This is an expository paper on the Quillen-Suslin Theorem, formerly known as Serre's Conjecture. A self-contained proof of this theorem is presented, followed by a discussion of the related Bass-Quillen Conjecture. The first chapter establishes the necessary theory, building on undergraduate algebra with the essentials of free, projective, and flat modules. The second chapter presents a complete proof of the theorem, dealing with regular rings, stably-free modules, and the related calculus of unimodular rows. The third and final chapter lists partial results surrounding the as yet unresolved Bass-Quillen Conjecture, offering brief explanations and suggestions for further reading. 1
Klíčová slova:
projektivní|modul|komutativní algebra|tenzor|okruhy polynomů; projective|module|commutative algebra|tensor product|polynomial ring