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A scheme over quasi-prime spectrum of modules | ||
| Journal of Algebra and Related Topics | ||
| مقاله 6، دوره 2، شماره 1، شهریور 2014، صفحه 65-77 اصل مقاله (175.83 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| A. Abbasi* ؛ D. Hassanzadeh-Lelekaami | ||
| University of Guilan | ||
| چکیده | ||
| 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 $M$. | ||
| کلیدواژهها | ||
| Quasi؛ Quasi-prime submodule؛ prime submodule؛ quasi-primeful module؛ primeful module؛ quasi-prime-embedding module؛ developed Zariski topology؛ prime؛ embedding module | ||
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