13A15 05C25 3 05C99 2 quasilocal ring 2 special principal ideal ring 2 zero-divisor graph 2 13A18 1 13B02 1 13C05 1 13C13 1 13F10 1 13H15 1 16D60 1 Clique number of a graph 1 Quasilocal ring 1 Special principal ideal ring 1 \(S\)-cotorsion-free module 1 \(S\)-second submodule 1 cancellation ideal 1 chromatic number 1 clique number of a graph 1 essential graph 1 ideal-based zero-divisor graph 1 local Artinian ring 1 planar graph 1 planar graphPlanar graph 1 pullback diagram 1 reduced ring 1 ring extension 1 second submodule 1