Let R be a commutative Noetherian ring and M be a finitely generated R-module. Considering the new concept of linkage of ideals over a module, we study the cohomological dimension of M with respect to the linked ideals over it.2010 Mathematics Subject Classification. 13C40, 13D45.
Let R = ⊕ n∈N0 R n be a standard graded ring, M be a finitely generated graded R-module and R + := ⊕ n∈N R n denotes the irrelevant ideal of R. In this paper, considering the new concept of linkage of ideals over a module, we study the graded components H i a (M ) n when a is an h-linked ideal over M . More precisely, we show that H i a (M ) is tame in each of the following cases:(i) i = f R+ a (M ), the first integer i for which R + 0 : H i a (M ); (ii) i = cd(R + , M ), the last integer i for which H i R+ (M ) = 0, and a = b + R + where b is an h-linked ideal with R + over M . Also, among other things, we describe the components H i a (M ) n where a is radically h-Mlicci with respect to R + of length 2.
Assume that R = ⊕ n∈N0 R n is a standard graded algebra over the local ring (R 0 , m 0 ), a is a homogeneous ideal of R, M is a finitely generated graded R-module and R + := ⊕ n∈N R n denotes the irrelevant ideal of R. In this paper, we study the asymptotic behaviour of the set {grade(a ∩ R 0 , H grade(R+,M) R+ (M ) n )} n∈Z as n → −∞, in the case where a and R + are homogenously linked over M .
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