Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

In the present paper, by considering the notion of MV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $Ksubseteq bigcup _{i=1}^{n}K_{i}$ implies $Ksubseteq K_{j...

We determine explicitly the Hodge ideals for determinant hypersurface as an intersection of symbolic powers determinantal ideals. prove our results by studying and weight filtrations on mixed module $$\mathcal {O}_{\mathscr {X}}(*\mathscr {Z})$$ regular functions space $$\mathscr {X}$$ $$n\times n$$ matrices, with poles along divisor {Z}$$ singular matrices. The composition factors filtration a...

For t in N, E.Miller has defined a category of positively t-determined modules over the polynomial ring S in n variables. We consider the AuslanderReiten translate, Nt, on the (derived) category of such modules. A monomial ideal I is t-determined if each generator x has a ≤ t. We compute the multigraded cohomology and betti spaces of N k t (S/I) for every iterate k and also the S-module structu...

In this paper, some results on vanishing and non-vanishing of generalized local cohomology modules are presented and some relations between those modules and, Ext and ordinary local cohomology modules are studied. Also, several cofiniteness propositions for generalized local cohomology modules are established which, among other things, provide an alternative answer to a question in [Y2].