Zariski subspace topologies on ideals

Year 2019, Volume: 48 Issue: 6, 1667 - 1674, 08.12.2019

Ortaç Öneş Mustafa Alkan

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

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