Prüfer conditions in amalgamated algebras

Abstract

In this article, we improve recent results on the transfer of Prüfer, Gaussian, and arithmetical conditions in amalgamated algebras. As an application we provide an answer to a question posed by Chhiti, Jarrar, Kabbaj, and Mahdou as well as we construct various examples.

Keywords:

• Amalgamated algebra
• arithmetical ring
• Gaussian ring
• Prüfer ring
• trivial extension

2010 Mathematics Subject Classification::

• Primary 13F05
• 13A15

Acknowledgments

The authors would like to thank the referee for his/her careful reading of the manuscript and several comments which greatly improved the article.