Mal'cev-Neumann rings and noncrossed product division algebras

2011/03/02 by Cécile Coyette, Coyette, Cécile
Mathematics · #16K20 #16S35 (primary) #16W60 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16K20 #msc:16S35 #msc:16W60

paper · pdf · doi:10.48550/arxiv.1103.0470

10 pages, submitted to Journal of Algebra and its Applications (JAA)

arxiv created 2011/03/02 · arxiv updated 2011/03/03

Abstract

We first give a sufficient condition for a Mal'cev-Neumann ring of formal series to be a noncrossed product division algebra. This result is then used to give an elementary proof of the existence of noncrossed product division algebras (of degree 8 or degree p² for p any odd prime).

Related

• A proof for a part of noncrossed product theorem
• Non cyclic division algebras of prime degree
• A note on Amitsur's noncrossed product theorem
• A Direct Approach to Noncrossed Product Division Algebras
• Commutator products in skew Laurent series division rings