Czechoslovak Mathematical Journal, first online, pp. 1-12
On $n$-2-absorbing ideals of commutative rings
Violeta LEOREANU-FOTEA
Received April 11, 2026. Published online September 15, 2026.
Abstract: The aim of this paper is to introduce and investigate a new class of ideals in commutative rings, called $n$-2-absorbing ideals, which extends the concept of $n$-ideals and is based on a conditioned triple-product absorption property. This definition fixes the algebraic roles of the components, causing the classes of $2$-absorbing ideals and $n$-2-absorbing ideals to diverge. We establish several characterizations and investigate their structural behavior under colon operations, ring homomorphisms, and chains of inclusions. Furthermore, we examine the stability of these ideals under standard algebraic constructions, including quotient rings, localization, Nagata's idealization, and the amalgamated duplication of a ring along an ideal.
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Affiliations: Violeta Leoreanu-Fotea Faculty of Mathematics, Al.I. Cuza University, Bd. Carol I, No. 11, 700506 Iaşi, Romania, e-mail: violeta.fotea@uaic.ro
