 This ring reflects many of the combinatorial properties of the simplicial complex, so it is of particular interest in algebraic combinatorics.In particular, the algebraic geometry of the Stanley–Reisner ring was used to characterize the numbers of faces in each dimension of simplicial polytopes.Every ring can be thought of as a monoid in Ab, the category of abelian groups (thought of as a monoidal category under the tensor product of formula_255-modules).