On Pseudo-valuation rings and their extensions

• Date: 2018
• Main Author: Bhat, V. K.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Automorphism; derivation; strongly prime ideal; divided prime ideal; pseudo-valuation ring; 16S36; 16N40; 16P40; 16S32
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/678
• Journal Title: Algebra and Discrete Mathematics

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...