Almost Condensed Domains

As an extension of the class of half condensed domains introduced by D.D. Anderson and Dumitrescu, we introduce and study the class of almost condensed domains. An integral domain D is almost condensed if whenever 0≠ z ∈ IJ with I; J ideals of D, there exist I′ ; J′ ideals of D such that I′ ⊆ I_w, J′ ⊆ J_w and zD = (I′ J′ )_w.