• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.669-689
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• 2020

Cohomological degrees (or extended degrees) were introduced by Doering, Gunston and Vasconcelos as measures for the complexity of structure of finitely generated modules over a Noetherian ring. Until now only very few examples of such functions have been known. Using a Cohen-Macaulay obstruction defined earlier, we construct an infinite family of cohomological degrees.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.471-477
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• 2019

Let (R, m) be a commutative Noetherian ring, I an ideal of R and M a non-zero finitely generated R-module. We show that if M and $H_0(I,M)$ are aCM R-modules and $I=(x_1,{\cdots},x_{n+1})$ such that $x_1,{\cdots},x_n$ is an M-regular sequence, then $H_i(I,M)$ is an aCM R-module for all i. Moreover, we prove that if R and $H_i(I,R)$ are aCM for all i, then R/(0 : I) is aCM. In addition, we prove that if R is aCM and $x_1,{\cdots},x_n$ is an aCM d-sequence, then depth $H_i(x_1,{\cdots},x_n;R){\geq}i-1$ for all i.