Kummer Spaces in Cyclic Algebras of Prime Degree

2014/10/22 by Adam Chapman, Chapman, Adam, David J. Grynkiewicz +8
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 16K20 #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Secondary 11J13 #math.RA #msc:11J13 #msc:16K20

paper · pdf · doi:10.48550/arxiv.1410.6136

12 pages

openalex publication_date 2014/10/22 · arxiv created 2015/05/14 · arxiv updated 2015/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the monomial Kummer subspaces of division cyclic algebras of prime degree p, showing that every such space is standard, and in particular the dimension is no greater than p+1. It follows that in a generic cyclic algebra, the dimension of any Kummer subspace is at most p+1.

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