D-modules over rings with finite F-representation type
S Takagi, R Takahashi - arXiv preprint arXiv:0706.3842, 2007 - arxiv.org
arXiv preprint arXiv:0706.3842, 2007•arxiv.org
Smith and Van den Bergh introduced the notion of finite F-representation type as a
characteristic $ p $ analogue of the notion of finite representation type. In this paper, we
prove two finiteness properties of rings with finite F-representation type. The first property
states that if $ R=\bigoplus_ {n\ge 0} R_n $ is a Noetherian graded ring with finite (graded) F-
representation type, then for every non-zerodivisor $ x\in R $, $ R_x $ is generated by $1/x $
as a $ D_ {R} $-module. The second one states that if $ R $ is a Gorenstein ring with finite F …
characteristic $ p $ analogue of the notion of finite representation type. In this paper, we
prove two finiteness properties of rings with finite F-representation type. The first property
states that if $ R=\bigoplus_ {n\ge 0} R_n $ is a Noetherian graded ring with finite (graded) F-
representation type, then for every non-zerodivisor $ x\in R $, $ R_x $ is generated by $1/x $
as a $ D_ {R} $-module. The second one states that if $ R $ is a Gorenstein ring with finite F …
Smith and Van den Bergh introduced the notion of finite F-representation type as a characteristic analogue of the notion of finite representation type. In this paper, we prove two finiteness properties of rings with finite F-representation type. The first property states that if is a Noetherian graded ring with finite (graded) F-representation type, then for every non-zerodivisor , is generated by as a -module. The second one states that if is a Gorenstein ring with finite F-representation type, then has only finitely many associated primes for any ideal of and any integer . We also include a result on the discreteness of F-jumping exponents of ideals of rings with finite (graded) F-representation type as an appendix.
arxiv.org
以上显示的是最相近的搜索结果。 查看全部搜索结果