2009/03/26 by Tim Neijens, Neijens, Tim, F. Van Oystaeyen +2
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA
paper · pdf · doi:10.48550/arxiv.0903.4640
arxiv created 2009/03/26 · openalex publication_date 2009/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first section of the paper, we will give some basic definitions and properties about Crystalline Graded Rings. In the following section we will provide a general description of the center. Afterwards, the case where the grading group is Abelian finite will be handled. The center will have some properties of a crystalline graded ring, but not all. We will call this Arithmetically Crystalline Graded. The center is crystalline graded if the part of degree zero is a principal ideal domain. The last section deals with the case where the grading group is non-Abelian finite. Since this situation is much more complicated than the Abelian case, we primarily focus on the conditions to have a trivial center. The fact that the center is Arithmetically Crystalline Graded also holds in this case.