The $\phi$-weak dimension of $\phi$-pseudo-valuation rings
UDC 512.5 It is shown that, for a strongly $\phi$-pseudo-valuation ring, which is nonnil-coherent, the only possible values of the $\phi$-weak global dimension are 0, 1, and $\infty.$ We then provide necessary and sufficient conditions for a strongly $\phi$-pseudo-valuation ring to be nonnil-coheren...
Збережено в:
| Дата: | 2026 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8299 |
| 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_ | 1860513019788787712 |
|---|---|
| author | Kim, Hwankoo Mahdou, Najib Oubouhou, El Houssaine Kim, Hwankoo Mahdou, Najib Oubouhou, El Houssaine |
| author_facet | Kim, Hwankoo Mahdou, Najib Oubouhou, El Houssaine Kim, Hwankoo Mahdou, Najib Oubouhou, El Houssaine |
| author_sort | Kim, Hwankoo |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:33:27Z |
| description | UDC 512.5
It is shown that, for a strongly $\phi$-pseudo-valuation ring, which is nonnil-coherent, the only possible values of the $\phi$-weak global dimension are 0, 1, and $\infty.$ We then provide necessary and sufficient conditions for a strongly $\phi$-pseudo-valuation ring to be nonnil-coherent. As an application of these findings, we demonstrate that if $R$ is a strongly nonnil-coherent $\phi$-pseudo-valuation ring, then any overring $B$ of $R$ is also a nonnil-coherent $\phi$-pseudo-valuation ring. |
| doi_str_mv | 10.3842/umzh.v77i8.8299 |
| first_indexed | 2026-03-24T03:38:02Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8299 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:38:02Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-82992026-03-21T13:33:27Z The $\phi$-weak dimension of $\phi$-pseudo-valuation rings The $\phi$-weak dimension of $\phi$-pseudo-valuation rings Kim, Hwankoo Mahdou, Najib Oubouhou, El Houssaine Kim, Hwankoo Mahdou, Najib Oubouhou, El Houssaine $\phi$-weak global dimension $\phi$-pseudo-valuation ring pseudo-valuation domain $\phi$-CR ring strongly $\phi$-ring UDC 512.5 It is shown that, for a strongly $\phi$-pseudo-valuation ring, which is nonnil-coherent, the only possible values of the $\phi$-weak global dimension are 0, 1, and $\infty.$ We then provide necessary and sufficient conditions for a strongly $\phi$-pseudo-valuation ring to be nonnil-coherent. As an application of these findings, we demonstrate that if $R$ is a strongly nonnil-coherent $\phi$-pseudo-valuation ring, then any overring $B$ of $R$ is also a nonnil-coherent $\phi$-pseudo-valuation ring. УДК 512.5 $\phi$-Слабка вимірність кілець $\phi$-псевдонормування Доведено, що для кільця сильного \(\phi\)-псевдонормування, яке є ненількогерентним, єдино можливі значення \(\phi\)-слабкої глобальної вимірності дорівнюють 0, 1 та \(\infty\). Одержано необхідні й достатні умови, за яких кільце сильного \(\phi\)-псевдонормування є ненількогерентним. Як застосування цих результатів показано, що якщо \(R\) --- сильно ненількогерентне кільце \(\phi\)-псевдонормування, то будь-яке надкільце \(B\) кільця \(R\) також є ненількогерентним кільцем \(\phi\)-псевдонормування. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8299 10.3842/umzh.v77i8.8299 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 8 (2025); 535 Український математичний журнал; Том 77 № 8 (2025); 535 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8299/10553 Copyright (c) 2025 Hwankoo Kim, Najib Mahdou, El Houssaine Oubouhou |
| spellingShingle | Kim, Hwankoo Mahdou, Najib Oubouhou, El Houssaine Kim, Hwankoo Mahdou, Najib Oubouhou, El Houssaine The $\phi$-weak dimension of $\phi$-pseudo-valuation rings |
| title | The $\phi$-weak dimension of $\phi$-pseudo-valuation rings |
| title_alt | The $\phi$-weak dimension of $\phi$-pseudo-valuation rings |
| title_full | The $\phi$-weak dimension of $\phi$-pseudo-valuation rings |
| title_fullStr | The $\phi$-weak dimension of $\phi$-pseudo-valuation rings |
| title_full_unstemmed | The $\phi$-weak dimension of $\phi$-pseudo-valuation rings |
| title_short | The $\phi$-weak dimension of $\phi$-pseudo-valuation rings |
| title_sort | $\phi$-weak dimension of $\phi$-pseudo-valuation rings |
| topic_facet | $\phi$-weak global dimension $\phi$-pseudo-valuation ring pseudo-valuation domain $\phi$-CR ring strongly $\phi$-ring |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8299 |
| work_keys_str_mv | AT kimhwankoo thephiweakdimensionofphipseudovaluationrings AT mahdounajib thephiweakdimensionofphipseudovaluationrings AT oubouhouelhoussaine thephiweakdimensionofphipseudovaluationrings AT kimhwankoo thephiweakdimensionofphipseudovaluationrings AT mahdounajib thephiweakdimensionofphipseudovaluationrings AT oubouhouelhoussaine thephiweakdimensionofphipseudovaluationrings AT kimhwankoo phiweakdimensionofphipseudovaluationrings AT mahdounajib phiweakdimensionofphipseudovaluationrings AT oubouhouelhoussaine phiweakdimensionofphipseudovaluationrings AT kimhwankoo phiweakdimensionofphipseudovaluationrings AT mahdounajib phiweakdimensionofphipseudovaluationrings AT oubouhouelhoussaine phiweakdimensionofphipseudovaluationrings |