A note on maximal ideals in ordered semigroups
In commutative rings having an identity element, every maximal ideal is a prime ideal, but the converse statement does not hold, in general. According to the present note, similar results for ordered semigroups and semigroups -without order- also hold. In fact, we prove that in commutative ordered s...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/951 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9512018-05-13T06:43:21Z A note on maximal ideals in ordered semigroups Kehayopulu, N. Ponizovskii, J. Tsingelis, M. maximal ideal, prime ideal in ordered semigroups 06F05 In commutative rings having an identity element, every maximal ideal is a prime ideal, but the converse statement does not hold, in general. According to the present note, similar results for ordered semigroups and semigroups -without order- also hold. In fact, we prove that in commutative ordered semigroups with identity each maximal ideal is a prime ideal, the converse statement does not hold, in general. Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/951 Algebra and Discrete Mathematics; Vol 2, No 1 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/951/480 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
maximal ideal prime ideal in ordered semigroups 06F05 |
| spellingShingle |
maximal ideal prime ideal in ordered semigroups 06F05 Kehayopulu, N. Ponizovskii, J. Tsingelis, M. A note on maximal ideals in ordered semigroups |
| topic_facet |
maximal ideal prime ideal in ordered semigroups 06F05 |
| format |
Article |
| author |
Kehayopulu, N. Ponizovskii, J. Tsingelis, M. |
| author_facet |
Kehayopulu, N. Ponizovskii, J. Tsingelis, M. |
| author_sort |
Kehayopulu, N. |
| title |
A note on maximal ideals in ordered semigroups |
| title_short |
A note on maximal ideals in ordered semigroups |
| title_full |
A note on maximal ideals in ordered semigroups |
| title_fullStr |
A note on maximal ideals in ordered semigroups |
| title_full_unstemmed |
A note on maximal ideals in ordered semigroups |
| title_sort |
note on maximal ideals in ordered semigroups |
| description |
In commutative rings having an identity element, every maximal ideal is a prime ideal, but the converse statement does not hold, in general. According to the present note, similar results for ordered semigroups and semigroups -without order- also hold. In fact, we prove that in commutative ordered semigroups with identity each maximal ideal is a prime ideal, the converse statement does not hold, in general. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/951 |
| work_keys_str_mv |
AT kehayopulun anoteonmaximalidealsinorderedsemigroups AT ponizovskiij anoteonmaximalidealsinorderedsemigroups AT tsingelism anoteonmaximalidealsinorderedsemigroups AT kehayopulun noteonmaximalidealsinorderedsemigroups AT ponizovskiij noteonmaximalidealsinorderedsemigroups AT tsingelism noteonmaximalidealsinorderedsemigroups |
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2024-04-12T06:26:23Z |
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2024-04-12T06:26:23Z |
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