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 $X:=\{Q\in q\Spec(M) \mid (Q:_R M)\in\Spec(R)\}$. 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 $M\rightarrow N$, and also by ring homomorphism $R\rightarrow S$. Among other results, we show that $(X, \mathcal{O}_X)$ is a scheme by putting some suitable conditions on $M$.
Abbasi, A. and Hassanzadeh-Lelekaami, D. (2014). A scheme over quasi-prime spectrum of modules. Journal of Algebra and Related Topics, 2(1), 65-77.
MLA
Abbasi, A. , and Hassanzadeh-Lelekaami, D. . "A scheme over quasi-prime spectrum of modules", Journal of Algebra and Related Topics, 2, 1, 2014, 65-77.
HARVARD
Abbasi, A., Hassanzadeh-Lelekaami, D. (2014). 'A scheme over quasi-prime spectrum of modules', Journal of Algebra and Related Topics, 2(1), pp. 65-77.
CHICAGO
A. Abbasi and D. Hassanzadeh-Lelekaami, "A scheme over quasi-prime spectrum of modules," Journal of Algebra and Related Topics, 2 1 (2014): 65-77,
VANCOUVER
Abbasi, A., Hassanzadeh-Lelekaami, D. A scheme over quasi-prime spectrum of modules. Journal of Algebra and Related Topics, 2014; 2(1): 65-77.
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