Work

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

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13050870

Authors: Nawaf L. Alsowait, Mohammed Al-Shomrani, Radwan M. Al-omary, Zakia Z. Al-Amery

Institutions: Northern Border University, King Abdulaziz University, Ibb University, University of Aden

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W4408219762

FWCI:

Cites: 14

Cited by:

Related to: 10