On Pseudo-valuation rings and their extensions
Let \(R\) be a commutative Noetherian \(\mathbb{Q}\)-algebra (\(\mathbb{Q}\)is the field of rational numbers). Let \(\sigma\) be an automorphism of \(R\) and \(\delta\) a \(\sigma\)-derivation of \(R\). We define a \(\delta\)-divided ring and prove the following: \((1)\)If \(R\) is a pseudo-valuati...
Збережено в:
| Дата: | 2018 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/678 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | Let \(R\) be a commutative Noetherian \(\mathbb{Q}\)-algebra (\(\mathbb{Q}\)is the field of rational numbers). Let \(\sigma\) be an automorphism of \(R\) and \(\delta\) a \(\sigma\)-derivation of \(R\). We define a \(\delta\)-divided ring and prove the following: \((1)\)If \(R\) is a pseudo-valuation ring such that \(x\notin P\) for any prime ideal \(P\) of \(R[x;\sigma,\delta]\), and \(P\cap R\) is a prime ideal of \(R\) with \(\sigma(P\cap R) = P\cap R\) and \(\delta(P\cap R) \subseteq P\cap R\), then \(R[x;\sigma,\delta]\) is also a pseudo-valuation ring. \((2)\)If \(R\) is a \(\delta\)-divided ring such that \(x\notin P\) for any prime ideal \(P\) of \(R[x;\sigma,\delta]\), and \(P\cap R\) is a prime ideal of \(R\) with \(\sigma(P\cap R) = P\cap R\) and \(\delta(P\cap R) \subseteq P\cap R\), then \(R[x;\sigma,\delta]\) is also a \(\delta\)-divided ring. |
|---|