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...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2003 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2003
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154673 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A note on maximal ideals in ordered semigroups / N. Kehayopulu, J. Ponizovskii, M. Tsingelis // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 32–35. — Бібліогр.: 3 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862570183302840320 |
|---|---|
| author | Kehayopulu, N. Ponizovskii, J. Tsingelis, M. |
| author_facet | Kehayopulu, N. Ponizovskii, J. Tsingelis, M. |
| citation_txt | A note on maximal ideals in ordered semigroups / N. Kehayopulu, J. Ponizovskii, M. Tsingelis // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 32–35. — Бібліогр.: 3 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-11-26T02:11:36Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154673 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T02:11:36Z |
| publishDate | 2003 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Kehayopulu, N. Ponizovskii, J. Tsingelis, M. 2019-06-15T17:39:26Z 2019-06-15T17:39:26Z 2003 A note on maximal ideals in ordered semigroups / N. Kehayopulu, J. Ponizovskii, M. Tsingelis // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 32–35. — Бібліогр.: 3 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 06F05. https://nasplib.isofts.kiev.ua/handle/123456789/154673 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics A note on maximal ideals in ordered semigroups Article published earlier |
| spellingShingle | A note on maximal ideals in ordered semigroups Kehayopulu, N. Ponizovskii, J. Tsingelis, M. |
| title | 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_short | A note on maximal ideals in ordered semigroups |
| title_sort | note on maximal ideals in ordered semigroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154673 |
| work_keys_str_mv | AT kehayopulun anoteonmaximalidealsinorderedsemigroups AT ponizovskiij anoteonmaximalidealsinorderedsemigroups AT tsingelism anoteonmaximalidealsinorderedsemigroups AT kehayopulun noteonmaximalidealsinorderedsemigroups AT ponizovskiij noteonmaximalidealsinorderedsemigroups AT tsingelism noteonmaximalidealsinorderedsemigroups |