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Let $(R,\mathfrak{m})$ 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 $I=(x_1, \ldots ,x_{n+1})$ such that $x_1, \ldots ,x_n$ 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 $x_1, \ldots ,x_n$ is an aCM $d$-sequence, then depth $H_i(x_1, \ldots ,x_n;R)\geq i-1$ for all $i$.
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참고문헌 (15)
참고문헌 신청
W. Bruns / 1993 / Cohen-Macaulay Rings / Cambridge University Press
L. Chu / 2015 / A note on almost Cohen-Macaulay modules / J. Algebra Appl 14(10):7
D. R. Grayson / Macaulay 2, a software system for research in algebraic geometry
C. Huneke / 1980 / On the symmetric and Rees algebra of an ideal generated by a d-sequence / J. Algebra 62(2):268~275
C. Huneke / 1982 / The theory of d-sequences and powers of ideals / Adv. in Math 46(3):249~279
L. Chu / 2015 / A note on almost Cohen-Macaulay modules / J. Algebra Appl 14(10):7
D. R. Grayson / Macaulay 2, a software system for research in algebraic geometry
C. Huneke / 1980 / On the symmetric and Rees algebra of an ideal generated by a d-sequence / J. Algebra 62(2):268~275
C. Huneke / 1982 / The theory of d-sequences and powers of ideals / Adv. in Math 46(3):249~279
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