In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationsh...In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationship between the Artinianness of HI^i（M, N） and the Artinianness of HI^i（N）. Then, we get that HI^d（M, N） is I-cofinite, if （R, m） is a d-dimensional Gorenstein local ring.展开更多
Let R be a Noetherian ring, M an Artinian R-module, and p ∈ CosRM. Thencograden. Homn（Rp, M） =-inf{i ｜πi（p, M） 〉 0} and πi（p, M） 〉 0 =〉 cogradeRpHomR（Rp, M） ≤ i ≤ fdRpHomR（Rp, M）,where πi （p,M） i...Let R be a Noetherian ring, M an Artinian R-module, and p ∈ CosRM. Thencograden. Homn（Rp, M） =-inf{i ｜πi（p, M） 〉 0} and πi（p, M） 〉 0 =〉 cogradeRpHomR（Rp, M） ≤ i ≤ fdRpHomR（Rp, M）,where πi （p,M） is the i-th dual Bass number of M with respect to p, cogradeRpHomR （Rp ,M） is the common length of any maxima[ HomR（Rp, M）-quasi co-regular sequence contained in pRp, and fdRp HomR（Rp, M） is the flat dimension of the Rp-module HomR（Rp, M）. We also study the relations among cograde, co-dimension and flat dimension of co-localization modules.展开更多
文摘In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationship between the Artinianness of HI^i（M, N） and the Artinianness of HI^i（N）. Then, we get that HI^d（M, N） is I-cofinite, if （R, m） is a d-dimensional Gorenstein local ring.
基金Partially supported by the National Natural Science Foundation of China （No. 11271275）.
文摘Let R be a Noetherian ring, M an Artinian R-module, and p ∈ CosRM. Thencograden. Homn（Rp, M） =-inf{i ｜πi（p, M） 〉 0} and πi（p, M） 〉 0 =〉 cogradeRpHomR（Rp, M） ≤ i ≤ fdRpHomR（Rp, M）,where πi （p,M） is the i-th dual Bass number of M with respect to p, cogradeRpHomR （Rp ,M） is the common length of any maxima[ HomR（Rp, M）-quasi co-regular sequence contained in pRp, and fdRp HomR（Rp, M） is the flat dimension of the Rp-module HomR（Rp, M）. We also study the relations among cograde, co-dimension and flat dimension of co-localization modules.
