Akademik Veri Yönetim Sistemi
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, cilt.2026, ss.1-18, 2026 (SCI-Expanded, Scopus)
Let R=⊕_{α∈Γ}R_{α} be a commutative integral domain graded by an arbitrary torsionless monoid Γ and let n be a positive integer. The paper explores the two concepts of graded n-powerful and graded n-powerful semiprimary ideals in graded integral domains, expanding the understanding of the ungraded context. It delves into the fundamental properties of these ideals, illustrating their distinctions from the ungraded counterpart and investigating their properties. We also introduce and study the concept of graded von Neumann regular rings, and we characterize some important classes of graded rings such as graded fields, graded von Neumann regular rings, graded strongly π-regular rings, graded principal ideal domains in terms of graded n-semiprimary ideals and graded semiprimary ideals.