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Let $(R,\m)$ be a Noetherian local Cohen-Macaulay ring and $I$ be a proper ideal of $R$. Assume that $\beta_R(I,R)$ denotes the constant value of ${\rm depth}_R(R/I^{n})$ for $n\gg0$. In this paper we introduce the new notion $\gamma_R(I,R)$ and then we prove the following inequalities: $$\beta_R(I,R)\leq\gamma_R(I,R)\leq \dim R - \cd(I,R)\leq \dim R/I.$$ Also, some applications of these inequalities will be included.
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참고문헌 (15)
참고문헌 신청
Kamal Bahmanpour / 2014 / Cohen-Macaulay modules over Noetherian local rings / 대한수학회보 51(2):373~386
Kamal Bahmanpour / 2015 / EXACTNESS OF IDEAL TRANSFORMS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES / 대한수학회지 52(6):1253~1270
Kamal Bahmanpour / 2018 / On the cohomological dimension of finitely generated modules / 대한수학회보 55(1):311~317
M. Brodmann / 1979 / Asymptotic Stability of Ass(M/I n M) / Proceedings of the American Mathematical Society 74(1):16~18
M. Brodmann / 1979 / The asymptotic nature of the analytic spread / Mathematical Proceedings of the Cambridge Philosophical Society 86(1):35~39
Kamal Bahmanpour / 2015 / EXACTNESS OF IDEAL TRANSFORMS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES / 대한수학회지 52(6):1253~1270
Kamal Bahmanpour / 2018 / On the cohomological dimension of finitely generated modules / 대한수학회보 55(1):311~317
M. Brodmann / 1979 / Asymptotic Stability of Ass(M/I n M) / Proceedings of the American Mathematical Society 74(1):16~18
M. Brodmann / 1979 / The asymptotic nature of the analytic spread / Mathematical Proceedings of the Cambridge Philosophical Society 86(1):35~39
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