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## Zariski subspace topologies on ideals

#### Ortaç ÖNEŞ [1] , Mustafa ALKAN [2]

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.
prime ideal, radical ideal, Zariski topology
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Primary Language en Mathematics Mathematics Orcid: 0000-0001-6777-9192Author: Ortaç ÖNEŞ (Primary Author)Institution: DEPARTMENT OF MATHEMATICSCountry: Turkey Orcid: 0000-0002-4452-4442Author: Mustafa ALKAN Institution: DEPARTMENT OF MATHEMATICSCountry: Turkey Publication Date : December 8, 2019
 Bibtex @research article { hujms656665, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1667 - 1674}, doi = {}, title = {Zariski subspace topologies on ideals}, key = {cite}, author = {ÖNEŞ, Ortaç and ALKAN, Mustafa} } APA ÖNEŞ, O , ALKAN, M . (2019). Zariski subspace topologies on ideals. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1667-1674 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/50516/656665 MLA ÖNEŞ, O , ALKAN, M . "Zariski subspace topologies on ideals". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1667-1674 Chicago ÖNEŞ, O , ALKAN, M . "Zariski subspace topologies on ideals". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1667-1674 RIS TY - JOUR T1 - Zariski subspace topologies on ideals AU - Ortaç ÖNEŞ , Mustafa ALKAN Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1667 EP - 1674 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Zariski subspace topologies on ideals %A Ortaç ÖNEŞ , Mustafa ALKAN %T Zariski subspace topologies on ideals %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R %U ISNAD ÖNEŞ, Ortaç , ALKAN, Mustafa . "Zariski subspace topologies on ideals". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1667-1674 . AMA ÖNEŞ O , ALKAN M . Zariski subspace topologies on ideals. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1667-1674. Vancouver ÖNEŞ O , ALKAN M . Zariski subspace topologies on ideals. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1674-1667.