On the S-spectrum of Krasner hypermodules
UDC 512.5 We study S-prime hyperideals by relating them to prime hyperideals. The S-prime hyperideals are studied in the hyperfield of fractions in the Krasner hyperring. The characterization of S-prime hyperideals is determined under a strong homomorphism. With the help of strong epimorphisms, the...
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| Datum: | 2026 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8348 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513060475633664 |
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| author | Aydın, Yıldız Nişancı Türkmen, Burcu Aydın, Yıldız Nişancı Türkmen, Burcu |
| author_facet | Aydın, Yıldız Nişancı Türkmen, Burcu Aydın, Yıldız Nişancı Türkmen, Burcu |
| author_sort | Aydın, Yıldız |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:34:09Z |
| description | UDC 512.5
We study S-prime hyperideals by relating them to prime hyperideals. The S-prime hyperideals are studied in the hyperfield of fractions in the Krasner hyperring. The characterization of S-prime hyperideals is determined under a strong homomorphism. With the help of strong epimorphisms, the conditions for one-to-one correspondence between the S-prime hyperideals in the hyperring and S-prime hyperideals in the hyperfield of fractions of these hyperrings are investigated. The concept of S-prime subhypermodules of Krasner hypermodules is introduced. In particular, the S-spectrum ${\rm Spec}_{S}$ of the S-Zariski topology is obtained, which is based on the element of S-prime subhypermodules of a class of these hypermodules. Moreover, characterizations of S-prime subhypermodules are given in the perspective of the S-spectrum. |
| doi_str_mv | 10.3842/umzh.v77i10.8348 |
| first_indexed | 2026-03-24T03:38:41Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8348 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:38:41Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-83482026-03-21T13:34:09Z On the S-spectrum of Krasner hypermodules On the S-spectrum of Krasner hypermodules Aydın, Yıldız Nişancı Türkmen, Burcu Aydın, Yıldız Nişancı Türkmen, Burcu Commutative hyperring, S-prime spectrum, S-Zariski topology. 16Y20, 13C05, 13C13, 16D80. UDC 512.5 We study S-prime hyperideals by relating them to prime hyperideals. The S-prime hyperideals are studied in the hyperfield of fractions in the Krasner hyperring. The characterization of S-prime hyperideals is determined under a strong homomorphism. With the help of strong epimorphisms, the conditions for one-to-one correspondence between the S-prime hyperideals in the hyperring and S-prime hyperideals in the hyperfield of fractions of these hyperrings are investigated. The concept of S-prime subhypermodules of Krasner hypermodules is introduced. In particular, the S-spectrum ${\rm Spec}_{S}$ of the S-Zariski topology is obtained, which is based on the element of S-prime subhypermodules of a class of these hypermodules. Moreover, characterizations of S-prime subhypermodules are given in the perspective of the S-spectrum. УДК 512.5 Про S-спектр гіпермодулів Краснера Досліджено S-простi гіперідеали за допомогою їхнього зв’язку з простими гіперідеалами. S-простi гіперідеали розглянуто в гіперполі дробів у гіперкільці Краснера. Встановлено характеризацію S-простих гіперідеалів при сильному гомоморфізмі. За допомогою сильних епіморфізмів досліджено умови взаємно однозначної відповідності між S-простими гіперідеалами у гіперкільці та S-простими гіперідеалами в гіперполі дробів цих гіперкілець. Уведено поняття S-простих підгіпермодулів гіпермодулів Краснера. Зокрема, побудовано S-спектр ${\rm Spec}_{S}$ S-циліндричної топології Заріскі, що ґрунтується на елементі S-простих підгіпермодулів певного класу таких гіпермодулів. Наведено також характеризації S-простих підгіпермодулів з точки зору S-спектра. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8348 10.3842/umzh.v77i10.8348 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 10 (2025); 640–641 Український математичний журнал; Том 77 № 10 (2025); 640–641 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8348/10567 Copyright (c) 2025 Yıldız Aydın, Burcu Nişancı Türkmen |
| spellingShingle | Aydın, Yıldız Nişancı Türkmen, Burcu Aydın, Yıldız Nişancı Türkmen, Burcu On the S-spectrum of Krasner hypermodules |
| title | On the S-spectrum of Krasner hypermodules |
| title_alt | On the S-spectrum of Krasner hypermodules |
| title_full | On the S-spectrum of Krasner hypermodules |
| title_fullStr | On the S-spectrum of Krasner hypermodules |
| title_full_unstemmed | On the S-spectrum of Krasner hypermodules |
| title_short | On the S-spectrum of Krasner hypermodules |
| title_sort | on the s-spectrum of krasner hypermodules |
| topic_facet | Commutative hyperring S-prime spectrum S-Zariski topology. 16Y20 13C05 13C13 16D80. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8348 |
| work_keys_str_mv | AT aydınyıldız onthesspectrumofkrasnerhypermodules AT nisancıturkmenburcu onthesspectrumofkrasnerhypermodules AT aydınyıldız onthesspectrumofkrasnerhypermodules AT nisancıturkmenburcu onthesspectrumofkrasnerhypermodules |