the notions of quasi-prime submodules and developed  zariski topology was introduced by the present authors in cite{ah10}. in this paper we use these notions to define a scheme. for an $r$-module $m$, let $x:={qin qspec(m) mid (q:_r m)inspec(r)}$. it is proved that $(x, mathcal{o}_x)$ is a locally ringed space. we study the morphism of locally ringed spaces induced by $r$-homomorphism $mrightar...

The aim of this paper is to give a detailed proof of a comparison of Voevodsky’s categories of geometric motives with and without transfers, respectively. The latter category is defined by means of h-topology introduced by Voevodsky, a topology essentially given by Zariski coverings, finite coverings and blowups.

Let $M$ and $N$ be two finitely generated graded modules over a standard graded Noetherian ring $R=bigoplus_{ngeq 0} R_n$. In this paper we show that if $R_{0}$ is semi-local of dimension $leq 2$ then, the set $hbox{Ass}_{R_{0}}Big(H^{i}_{R_{+}}(M,N)_{n}Big)$ is asymptotically stable for $nrightarrow -infty$ in some special cases. Also, we study the torsion-freeness of graded generalized local ...

Let $K$ be a field. The \'etale open topology on the $K$-points $V(K)$ of $K$-variety $V$ was introduced in our previous work. is non-discrete if and only large. If separably, real, $p$-adically closed then agrees with Zariski, order, valuation topology, respectively. We show that existentially definable sets perfect large fields behave well respect to this topology: such are finite unions subs...

We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

The notions of quasi-prime submodules and developed  Zariski topology was introduced by the present authors in cite{ah10}. In this paper we use these notions to define a scheme. For an $R$-module $M$, let $X:={Qin qSpec(M) mid (Q:_R M)inSpec(R)}$. It is proved that $(X, mathcal{O}_X)$ is a locally ringed space. We study the morphism of locally ringed spaces induced by $R$-homomorphism $Mrightar...

Here we take the view that small abelian categories are certain categorical versions of rings and the collection of Serre subcategories of a small abelian category is then analogous to the set of ideals of a commutative ring. We consider two topologies on the collection of Serre subcategories; one is a very direct lift of the Zariski topology, the other, dual, topology appeared in the context o...

For a module M over commutative ring R with identity, let RSpec(M) denote the collection of all submodules L Msuch that ?(L:M) is prime ideal and equal to (rad L:M). In this article, we topologies topology which enjoys analogs many properties Zariski on spectrum Spec(M) (as subspace topology). We investigate topological space from point view spectral spaces by establishing interrelations betwee...