The strongly irreducible dimension of rings vs. the derived dimension of the space of strongly irreducible ideals with V-topology
نویسندگان
1 Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
2 Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
doi
10.22034/as.2024.21459.1710چکیده
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 $1$.
