A source of semiprimeness on inverse and completely regular semigroups
UDC 512.5 We define $|S_{S}|$-inverse semigroup and $|S_{S}|$-completely regular semigroup structures that are not encountered in the literature and are studied in our work for the first time. The properties of these new semigroup types and their relations with the other semigroup types...
Збережено в:
| Дата: | 2024 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2024
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7699 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512702113251328 |
|---|---|
| author | Mekera, Rasie Yeşil, Didem Mekera, Rasie Yeşil, Didem |
| author_facet | Mekera, Rasie Yeşil, Didem Mekera, Rasie Yeşil, Didem |
| author_sort | Mekera, Rasie |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-02-11T07:12:31Z |
| description | UDC 512.5
We define $|S_{S}|$-inverse semigroup and $|S_{S}|$-completely regular semigroup structures that are not encountered in the literature and are studied in our work for the first time. The properties of these new semigroup types and their relations with the other semigroup types, such as $|S_{S}|$-idempotent, $|S_{S}|$-regular, $|S_{S}|$-nonzero, and $|S_{S}|$-reduced semigroups, are discussed. Further, the relationship between the source of semiprimeness and the semiprime ideal is analyzed. It is also shown that the intersection of all semiprime ideals is equal to the source of semiprimeness. Moreover, if a function is surjective, then it can be shown that the analyzed two structures are preserved under homomorphism. |
| doi_str_mv | 10.3842/umzh.v76i8.7699 |
| first_indexed | 2026-03-24T03:32:59Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7699 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:59Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-76992025-02-11T07:12:31Z A source of semiprimeness on inverse and completely regular semigroups A source of semiprimeness on inverse and completely regular semigroups Mekera, Rasie Yeşil, Didem Mekera, Rasie Yeşil, Didem Regular semigroup completely regular semigroups inverse semigroup semiprime semigroup UDC 512.5 We define $|S_{S}|$-inverse semigroup and $|S_{S}|$-completely regular semigroup structures that are not encountered in the literature and are studied in our work for the first time. The properties of these new semigroup types and their relations with the other semigroup types, such as $|S_{S}|$-idempotent, $|S_{S}|$-regular, $|S_{S}|$-nonzero, and $|S_{S}|$-reduced semigroups, are discussed. Further, the relationship between the source of semiprimeness and the semiprime ideal is analyzed. It is also shown that the intersection of all semiprime ideals is equal to the source of semiprimeness. Moreover, if a function is surjective, then it can be shown that the analyzed two structures are preserved under homomorphism. УДК 512.5 Джерело напівпростоти на обернених та цілком регулярних напівгрупах Визначено $|S_{S}|$-інверсні напівгрупові та $|S_{S}|$-повністю регулярні напівгрупові структури, які не зустрічаються в літературі та досліджуються вперше. Розглянуто властивості цих нових типів напівгруп та їхні зв’язки з іншими типами напівгруп, такими як $|S_{S}|$-ідемпотентні, $|S_{S}|$-регулярні, $|S_{S}|$-ненульові та $|S_{S}|$-редуковані. Крім того, проаналізовано зв’язок між джерелом напівпростоти та напівпростим ідеалом, а також показано, що перетин усіх напівпростих ідеалів дорівнює джерелу напівпростоти. Більш того, для сур'єктивної функції показано, що ці дві структури зберігаються при гомоморфізмі. Institute of Mathematics, NAS of Ukraine 2024-09-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7699 10.3842/umzh.v76i8.7699 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 8 (2024); 1254 - 1259 Український математичний журнал; Том 76 № 8 (2024); 1254 - 1259 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7699/10159 Copyright (c) 2024 Rasie Mekera |
| spellingShingle | Mekera, Rasie Yeşil, Didem Mekera, Rasie Yeşil, Didem A source of semiprimeness on inverse and completely regular semigroups |
| title | A source of semiprimeness on inverse and completely regular semigroups |
| title_alt | A source of semiprimeness on inverse and completely regular semigroups |
| title_full | A source of semiprimeness on inverse and completely regular semigroups |
| title_fullStr | A source of semiprimeness on inverse and completely regular semigroups |
| title_full_unstemmed | A source of semiprimeness on inverse and completely regular semigroups |
| title_short | A source of semiprimeness on inverse and completely regular semigroups |
| title_sort | source of semiprimeness on inverse and completely regular semigroups |
| topic_facet | Regular semigroup completely regular semigroups inverse semigroup semiprime semigroup |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7699 |
| work_keys_str_mv | AT mekerarasie asourceofsemiprimenessoninverseandcompletelyregularsemigroups AT yesildidem asourceofsemiprimenessoninverseandcompletelyregularsemigroups AT mekerarasie asourceofsemiprimenessoninverseandcompletelyregularsemigroups AT yesildidem asourceofsemiprimenessoninverseandcompletelyregularsemigroups AT mekerarasie sourceofsemiprimenessoninverseandcompletelyregularsemigroups AT yesildidem sourceofsemiprimenessoninverseandcompletelyregularsemigroups AT mekerarasie sourceofsemiprimenessoninverseandcompletelyregularsemigroups AT yesildidem sourceofsemiprimenessoninverseandcompletelyregularsemigroups |