Order complex of ideals in a commutative ring with identity

Independence complexes of comaximal graphs of commutative rings with identity

“…Proof. The proof is completely analogous to the proof in [7] which we give here for the sake of completeness. It applies for both complexes so let Ind stand for both Ind H ′ (R) and Ind Γ ′ 2 (R) .…”

“…In general, the idea of associating a combinatorial object to a commutative ring with identity has been of great interest to researches, so for other examples of associating a graph to a commutative ring the reader may wish to consult [1,2,3,10,13]. For another example of associating simplicial complexes to commutative rings, we refer the reader to [7] where the authors associated order complex with a general commutative ring via chains of ideals following a suggestion from Vassiliev in [12], and determined homotopy type of that complex.…”

Ideal zero-divisor complex

“…For another example of associating simplicial complexes to commutative rings, the reader may wish to consult [9], where the authors associated order complex with a general commutative ring via chains of ideals and they had determined the homotopy type of that complex.…”