| Abstrakt: |
Let * be a star-operation of finite type on an integral domainD. In this paper, we generalize and study the concept of almost splitting sets. We define a saturated multiplicative subsetSofDto be an almost g*-splitting set ofDif for each 0 ≠ d ∈ D, there exists an integern = n(d) ≥1 such thatdn = stfor somes ∈ Sandt ∈ Dwith (t,s′)* = Dfor alls′ ∈ S. Among other things, we prove that every saturated multiplicative subset ofDis an almostg*-splitting set if and only ifDis an almost weakly factorial domain (AWFD) with *-dim (D) = 1. We also give an example of an almost g*-splitting set which is not a g*-splitting set. [ABSTRACT FROM AUTHOR] |
