Work

Weakly S-square-difference factor absorbing ideals in commutative rings

Year: 2026

Type: article

Abstract: We develop the theory of weakly S -square-difference factor absorbing ideals (weakly S -sdf ideals) in a commutative ring R , extending the notion of weakly sdf-absorbing ideals to a relative setting determined by a multiplicatively closed subset $$S\subseteq R$$ S ⊆ R . We establish their basic properties, relate them to weakly S -prime, S -sdf-absorbing, and S -semiprime ideals, and use the S -characteristic and S -invertible elements to identify conditions under which weakly S -sdf ideals strengthen to weakly S -prime or S -sdf-absorbing ideals. We further examine their behavior under homomorphic images, direct products, quotients, trivial ring extensions, amalgamated duplications, and amalgamated algebras. A complete characterization of weakly S -sdf ideals in pullback rings $$A\times _{C}B$$ A × C B is obtained, showing that the property transfers precisely through the coordinate ideals together with a natural square-difference compatibility condition.

Source: ANNALI DELL UNIVERSITA DI FERRARA

DOI: 10.1007/s11565-026-00646-z

Authors: Alaa Abouhalaka, Hwankoo Kim

Institutions: Ministry of Education and Higher Education, Cukurova University, Hoseo University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: National Research Foundation, National Research Foundation of Korea, Qatar National Library