The Center of Crystalline Graded Rings
Abstract
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.
Keywords
Cite
@article{arxiv.0903.4640,
title = {The Center of Crystalline Graded Rings},
author = {Tim Neijens and Fred Van Oystaeyen},
journal= {arXiv preprint arXiv:0903.4640},
year = {2009}
}