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arXiv · 1602.04174

Rings satisfying *-property

Kursat Hakan Oral·Bayram Ali Ersoy·Unsal Tekir
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Abstract

In this paper we will investigate commutative rings which have the $\ast $-property. We say that a ring $R$ satisfy $\ast-$property if for any family of ideals $\left\{ I_{\alpha}\right\} _{\alpha\in S}$ of $R$ in which $S$ is an index set, there exists a finite subset\ $S^{\prime}$ of $S$ such that the radical of the intersection of the family of ideals $\left\{ I_{\alpha}\right\} _{\alpha\in S}$ is equal to the intersection of the radicals of ideals $\left\{ I_{\alpha}\right\} _{\alpha\in S^{\prime}}$ . We will show that any integral domain which satisfy $\ast-$property is a field. Furthermore, these rings are zero-dimensional. After this we give relations between these rings and Artinian rings.

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Kursat Hakan Oral, Bayram Ali Ersoy, Unsal Tekir. 2016-02-12. Rings satisfying *-property. https://arxiv.org/abs/1602.04174

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