%0 Journal Article
%T A scheme over quasi-prime spectrum of modules
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Abbasi, A.
%A Hassanzadeh-Lelekaami, D.
%D 2014
%\ 06/01/2014
%V 2
%N 1
%P 65-77
%! A scheme over quasi-prime spectrum of modules
%K Quasi
%K Quasi-prime submodule
%K prime submodule
%K quasi-primeful module
%K primeful module
%K quasi-prime-embedding module
%K developed Zariski topology
%K prime
%K embedding module
%R
%X 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 $Mrightarrow N$, and also by ring homomorphism $Rrightarrow S$. Among other results, we show that $(X, mathcal{O}_X)$ is a scheme by putting some suitable conditions on $M$.
%U https://jart.guilan.ac.ir/article_61_25bfba65b52ff4402f27084e6c3383e8.pdf