Bulletin of the
Korean Mathematical Society BKMS

Let R be a commutative ring with identity and m, n be positive
integers. In this paper, we introduce the class of weakly (m; n)-prime ideals
generalizing (m; n)-prime and weakly (m; n)-closed ideals. A proper ideal I of
R is called weakly (m; n)-prime if for a; b 2 R, 0 6= amb 2 I implies either an 2
I or b 2 I: We justify several properties and characterizations of weakly (m; n)-
prime ideals with many supporting examples. Furthermore, We investigate
weakly (m; n)-prime ideals under various contexts of constructions such as
direct products, localizations and homomorphic images. Finally, we discuss
the behaviour of this class of ideals in idealization and amalgamated rings.

Keywords: Weakly (m; n)-prime ideal, weakly (m; n)-closed ideal, (m; n)-prime ideal, weakly n-absorbing ideal.

MSC numbers: 13A15, 13F05.