We consider an homogeneous ideal I in the polynomial ring $$S=K[x_1,\dots ,$$ $$x_m]$$ over a finite field $$K={\mathbb {F}}_q$$ and set of projective rational points $${{\mathbb {X}}}$$ that it defines space {P}}}^{m-1}$$ . concern ourselves with problem computing vanishing $$I({{\mathbb {X}}})$$ This is usually done by adding equations {P}}}^{m-1})$$ to radical. give alternative more efficien...

of an m-primary ideal a⊆ R. In fact, if qm = a for a fixed ideal a then it is evident that e(a)= vol(v). The volume of a valuation has implicitly been studied already in [4], but it was first explicitly defined in [5]. The terminology is intended to emphasize the relation with global invariants of linear series on projective varieties. A natural question is to what extent the properties of vol(...

We provide solutions to several problems of Foreman about ideals, several of which are closely related to Mitchell’s notion of strongly proper forcing. We prove: (1) Presaturation of a normal ideal implies projective antichain catching, enabling us to provide a solution to a problem from Foreman [8] about ideal projections which is more comprehensive and simpler than the solution obtained in [4...

Let ρC be the regularity of the Hilbert function of a projective space curve C over an algebraically closed field, αI be the initial degree of the defining ideal I of C and βI the least degree t such that the depth of the ideal generated by I≤t is depth(I). Then the Castelnuovo-Mumford regularity reg(C) of C is upper bounded by max{ρC +1, αI +βI −1}. We study in deep and refine the above bound ...

The Orlik-Solomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E . At first we study homological properties of E-modules as e.g. complexity, depth and regularity. In particular, we consider modules with linear injective resolutions. We apply our results to Orlik-Solomon algebras of matroids and give formulas for the complexity, depth and regularity of such...

Let be a module over commutative ring with identity. Before studying the concept of Strongly Pseudo Nearly Semi-2-Absorbing submodule, we need to mention ideal and basics that you study submodule. Also, introduce several characteristics submodule in classes multiplication modules other types modules. We also had no luck because is not ideal. it noted under conditions, which this faithful module...

Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

In this paper $S$ is a monoid with a left zero and $A_S$ (or $A$) is a unitary right $S$-act. It is shown that a monoid $S$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $S$-act is quasi-projective. Also it is shown that if every right $S$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...