Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P-1 is a ring. In fact, it is proved that P-1 = (P : P) if and only if P is not invertible. Furthermore, if P is invertible, then R = (P : P) and P is a principal ideal of R.

In this paper, prime ideal bundles and semi-prime and irreducible ideal bundles of a Lie algebra bundle are defined and their relation with prime ideal bundles is studied.

In this paper, we introduce the concepts of J-prime ideals and MJ-ideals in posets, and obtain some of their interesting characterizations in posets. Furthermore, we discuss the properties of J-ideals that are analogous to J-prime ideals and MJ-ideals in posets. Finally, we establish a set of equivalent conditions for an ideal in a poset P containing an ideal J is an J-ideal, and for a semi-prime ideal J to be an MJ-ideal of P.

In this paper we introduce the notion of multiplication ideals in Γ-rings and we obtain some characterizations for multiplication ideals in Γ-rings.

Let G be a , nitely generated abelian group and M be a G-graded A-module. In general, G-associated prime ideals to M may not exist. In this paper, we introduce the concept of G-attached prime ideals to M as a generalization of G-associated prime ideals which gives a connection between certain G-prime ideals and G-graded modules over a (not necessarily G-graded Noetherian) ring. We prove that the G-attached prime ideals exist for every nonzero G-graded module and this generalization is proper. We transfer many results of G-associated prime ideals to G-attached prime ideals and give some applications of it.