The $$\mathfrak a$$-filter Grade of an Ideal $$\mathfrak b$$ and $$(\mathfrak a,\mathfrak b)$$-f-modules

Abstract

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 f-gradR( $$\mathfrak a,\mathfrak b$$ ,M) which was introduced in [Bull. Malays. Math. Sci. Soc., 2015, 38(2): 467–482]. Some computations and bounds of f-gradR( $$\mathfrak a,\mathfrak b$$ ,M) are provided. We also give the structure of ( $$\mathfrak a,\mathfrak b$$ )-f-modules. Some properties which are analogous to those of Cohen-Macaulay modules are discovered.