A scheme over quasi-prime spectrum of modules

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Abstract:

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 $M$.

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Journal title

volume 2  issue 1

pages  65- 77

publication date 2014-06-01

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