(2022-12-01) ASLANKARAYİĞİT UĞURLU, EMEL; Anebri A., Mahdou N., ASLANKARAYİĞİT UĞURLU E.
Let R be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of n-ideals and the class of (2, n)-ideals. A proper ideal I of R is said to be a quasi n-ideal if root I is an n-ideal of R. Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the n-ideals, the quasi primary ideals, the (2, n)-ideals and the pr-ideals. Moreover, we use the quasi n-ideals to characterize some kind of rings. Finally, we investigate quasi n-ideals under various contexts of constructions such as direct product, power series, idealization, and amalgamation of a ring along an ideal.