2013/08/29 by Renato Fehlberg Júnior, Júnior, Renato Fehlberg
Mathematics · #16K40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1308.6602
openalex publication_date 2013/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Makar-Limanov's conjecture states that if a division ring D is finitely generated and infinite dimensional over its center k then D contains a free k-subalgebra of rank 2. In this work, we will investigate the existence of such structures in D, the division ring of fractions of the skew polynomial ring L[t;σ], where t is a variable and σ is a k-automorphism of L. For instance, we prove Makar-Limanov's conjecture when either L is the function field of an abelian variety or the function field of the n-dimensional projective space.