The strongly irreducible dimension of rings vs. the derived dimension of the space of strongly irreducible ideals with V-topology

An ideal I of a ring R is called strongly irreducible ideal (SI-ideal, for short), whenever the inclusion J\cap K\subseteq I, implies that J\subseteq I or K\subseteq I. Let X={\rm SSpec}(R) be the set of all strongly irreducible ideals of a ring R. Then X with certain topology has derived dimension if and only if R has strongly irreducible dimension. Moreover, the two dimensions differ by at most ۱.

کلیدواژه ها:

Arithmetical ring ، Derived dimension ، Strongly irreducible ideal ، Strongly regular ring ، V-topology