Commutatively closed sets in rings

Abstract

Encompassing many standard notions such as Dedekind finite and reversible rings we introduce and study a new property for subsets of a ring. We give many examples and characterize some rings such as 2-primal rings with the aid of this notion.

Keywords:

• Commutatively closed
• reversible
• Dedekind finite
• commutative closure

2010 Mathematics Subject Classification:

• 16U80
• 16U70

Acknowledgements

The first author would like to thank her supervisor Prof. A. Leroy for his continuous guidance and help during the preparation of this text that will be part of her Ph.D. Thesis. She would also like to thank King Abdulaziz University (Saudi Arabia) for the financial support received during the preparation of this article and the University of Artois for welcoming her during all these years. We warmly thank P. Nielsen and the referee for carefully reading and commenting a first version of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.