On a Quotient Ring That Satisfies Certain Identities via Generalized Reverse Derivations

Nawaf L. Alsowait, Mohammed Al-Shomrani, Radwan M. Al-omary () and Zakia Z. Al-Amery
Additional contact information
Nawaf L. Alsowait: Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia
Mohammed Al-Shomrani: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Radwan M. Al-omary: Department of Mathematics, Ibb University, Ibb 70270, Yemen
Zakia Z. Al-Amery: Department of Mathematics, Aden University, Aden 5243, Yemen

Mathematics, 2025, vol. 13, issue 5, 1-12

Abstract: In this article, for a prime ideal ρ of an arbitrary ring ℜ, we study the commutativity of the quotient ring ℜ / ρ , whenever ℜ admits a generalized reverse derivation ϑ associated with a reverse derivation ∂ that satisfies certain identities in ρ . Additionally, we show that, for some cases, the range of the generalized reverse derivation ϑ lies in the prime ideal ρ . Moreover, we explore several consequences and special cases. Throughout, we provide examples to demonstrate that various restrictions in the assumptions of our results are essential.

Keywords: prime ideal; integral domain; generalized reverse derivation; quotient ring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/5/870/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/5/870/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:5:p:870-:d:1606101

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().