ABSORBING IDEALS IN COMMUTATIVE RINGS: AN APPLICATION IN TOPOLOGICAL GROUP ACTION THEORY

We present a certain theoretical construction with the so-called absorbing ideals in commutative rings, which were systematically defined and studied by D. F. Anderson and A. Badawi (2011). We present a construction using tolls of the absorbing ideal theory in commutative rings and an application in topological group action theory. More precisely, we are going to study certain primitive group actions on collections of proper ideals of commutative rings. Furthermore, we will classify geometrically all irreducible affine varieties for which the collection of radical ideals of its coordinate ring is under a certain primitive group action.