论文标题
$ \ mathfrak {a} $ - 理想$ \ mathfrak {b} $和$（\ mathfrak {a}，\ mathfrak {b}）$ - $ \ mathrm {f} $ - 模块模块
The $\mathfrak{a}$-Filter grade of an ideal $\mathfrak{b}$ and $(\mathfrak{a},\mathfrak{b})$-$\mathrm{f}$-modules
论文作者
论文摘要
令$ \ mathfrak {a}，\ mathfrak {b} $是交换性noetherian run $ r $和$ m $有限生成的$ r $ -module的两个理想。〜我们继续学习$ \ textrm {f} \ textrm { - } \ mathrm {grad} _r（\ mathfrak {a}，\ mathfrak {b}，m）$，该$在[bull中引入。马来人。数学。科学。 Soc。 38（2015）467--482]，$ \ textrm {f} \ textrm { - } \ mathrm {grad} _r（\ mathfrak {a}，\ mathfrak {b}，m）$的某些计算和边界。 $（\ mathfrak {a}，\ mathfrak {b}）$ - $ \ mathrm {f} $ - 模块，〜与Cohen Macaulay模块相似的各种属性。
Let $\mathfrak{a},\mathfrak{b}$ be two ideals of a commutative noetherian ring $R$ and $M$ a finitely generated $R$-module.~We continue to study $\textrm{f}\textrm{-}\mathrm{grad}_R(\mathfrak{a},\mathfrak{b},M)$ which was introduced in [Bull. Malays. Math. Sci. Soc. 38 (2015) 467--482], some computations and bounds of $\textrm{f}\textrm{-}\mathrm{grad}_R(\mathfrak{a},\mathfrak{b},M)$ are provided.~We also give the structure of $(\mathfrak{a},\mathfrak{b})$-$\mathrm{f}$-modules,~various properties which are analogous to those of Cohen Macaulay modules are discovered.
