Questions about commutative rings, their ideals, and their modules.

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If $G$ is shellable, then $G \backslash \{x_i\}$ is shellable?

A simplicial complex $\Delta$ on the vertex set $\{x_1,\dots,x_n\}$ is shellable if the facets of $\Delta$ can be ordered, say $F_ 1 , . . . , F _s$, such that for all $1 \leq i < j ...