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 order...
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| Дата: | 2003 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2003
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-154673 |
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dspace |
| spelling |
irk-123456789-1546732019-06-16T01:32:45Z A note on maximal ideals in ordered semigroups Kehayopulu, N. Ponizovskii, J. Tsingelis, M. 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. 2003 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/154673 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Kehayopulu, N. Ponizovskii, J. Tsingelis, M. |
| spellingShingle |
Kehayopulu, N. Ponizovskii, J. Tsingelis, M. A note on maximal ideals in ordered semigroups Algebra and Discrete Mathematics |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2003 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154673 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
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| first_indexed |
2023-05-20T17:45:12Z |
| last_indexed |
2023-05-20T17:45:12Z |
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1796154009197740032 |