2022/10/01 by Hani A. Khashan, Khashan, Hani A., Ece Yetki̇n Çeli̇kel +1 · 1 citation
Computer Science · Mathematics · #16P40 #Advanced Algebra and Logic #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13A15 #Rings, Modules, and Algebras #Secondary 16D60
paper · pdf · doi:10.48550/arxiv.2210.00249
openalex publication_date 2022/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For commutative rings with identity, we introduce and study the concept of semi r-ideals which is a kind of generalization of both r-ideals and semiprime ideals. A proper ideal I of a commutative ring R is called semi r-ideal if whenever a2∈ I and AnnR(a)=0, then a∈ I. Several properties and characterizations of this class of ideals are determined. In particular, we investigate semi r-ideal under various contexts of constructions such as direct products, localizations, homomorphic images, idealizations and amalagamations rings. We extend semi r-ideals of rings to semi r-submodules of modules and clarify some of their properties. Moreover, we define submodules satisfying the D-annihilator condition and justify when they are semi r-submodules.