Akademik Veri Yönetim Sistemi
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.2026, ss.1-16, 2026 (SCI-Expanded, Scopus)
Let R be a commutative ring with 1≠0 and n be a fixed positive integer. A proper ideal I of R is said to be an n-OA ideal if whenever a1a2⋯an+1∈I for some nonunits a1,a2,…,an+1∈R, then a1a2⋯an∈I or an+1∈I. A commutative ring R is said to be an n-OAF ring if every proper ideal I of R is a product of finitely many n-OA ideals. In fact, 1-OAF rings and 2-OAF are exactly the general ZPI rings and OAF rings, respectively. In addition to giving various properties of n-OAF rings, we give a characterization of Noetherian von Neumann regular rings in terms of our new concept. Furthermore, we investigate the n-OAF property of some extension of rings such as the polynomial ring R[X], the formal power series ring R[[X]], the ring of A+XB[X], and the trivial extension R=A∝E of an A-module E.