Zariski subspace topologies on ideals

Authors : Ortaç ÖNEŞ, Mustafa ALKAN

Pages : 1667-1674

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Publication Date : 2019-12-08

Article Type : Research Paper

Abstract :In this paper, we show how there are tight relationships between algebraic properties of a commutative ring $R$ and topological properties of open subsets of Zariski topology on the prime spectrum of $R$. We investigate some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense and irreducible. We also give a characterization for the radical of an ideal in $R$ by using topological properties.
Keywords : prime ideal, radical ideal, Zariski topology