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## $k$-Congruences and the Zariski topology in semirings

#### Song-chol HAN [1]

The purpose of this paper is to study topological properties of both the set of all $k$-prime ideals and the set of all $k$-prime congruences for any commutative semiring with zero and identity. We first prove that the $k$-prime spectrum, i.e. the set of all $k$-prime ideals equipped with the Zariski topology is a spectral space, and then prove that the set of all $k$-prime congruences is homeomorphic to the $k$-prime spectrum with respect to their Zariski topologies.
semiring, ideal, congruence, prime ideal, Zariski topology
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-3846-5749Author: Song-chol HAN (Primary Author)Institution: Kim Il Sung UniversityCountry: North Korea Publication Date : June 7, 2021
 Bibtex @research article { hujms614688, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {699 - 709}, doi = {10.15672/hujms.614688}, title = {\$k\$-Congruences and the Zariski topology in semirings}, key = {cite}, author = {Han, Song-chol} } APA Han, S . (2021). $k$-Congruences and the Zariski topology in semirings . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 699-709 . DOI: 10.15672/hujms.614688 MLA Han, S . "$k$-Congruences and the Zariski topology in semirings" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 699-709 Chicago Han, S . "$k$-Congruences and the Zariski topology in semirings". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 699-709 RIS TY - JOUR T1 - $k$-Congruences and the Zariski topology in semirings AU - Song-chol Han Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.614688 DO - 10.15672/hujms.614688 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 699 EP - 709 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.614688 UR - https://doi.org/10.15672/hujms.614688 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics $k$-Congruences and the Zariski topology in semirings %A Song-chol Han %T $k$-Congruences and the Zariski topology in semirings %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.614688 %U 10.15672/hujms.614688 ISNAD Han, Song-chol . "$k$-Congruences and the Zariski topology in semirings". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 699-709 . https://doi.org/10.15672/hujms.614688 AMA Han S . $k$-Congruences and the Zariski topology in semirings. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 699-709. Vancouver Han S . $k$-Congruences and the Zariski topology in semirings. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 699-709. IEEE S. Han , "$k$-Congruences and the Zariski topology in semirings", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 699-709, Jun. 2021, doi:10.15672/hujms.614688

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