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Combinatorial invariance of Stanley-Reisner rings. (English) Zbl 0872.55018
The authors prove the following result: Let $$k$$ be a field and $$\Delta$$, $$\Delta'$$ be two abstract simplicial complexes defined at the vertex sets $$V=\{v_1,\dots,v_n\}$$ and $$U=\{u_1,\dots,u_n\}$$, respectively. Suppose $$k[\Delta]$$ and $$k[\Delta']$$, the associated Stanley-Reisner rings, are isomorphic as $$k$$-algebras. Then there exists a bijective mapping $$\psi:V\to U$$ which induces an isomorphism between $$\Delta$$ and $$\Delta'$$.

##### MSC:
 55U05 Abstract complexes in algebraic topology 13G05 Integral domains
##### Keywords:
abstract simplicial complexes; Stanley-Reisner rings
Full Text:
##### References:
 [1] W. Bruns and J. Herzog, Cohen-Macaulay Rings.Cambridge Studies in Advanced Mathematics 39,Cambridge University Press,Cambridge, 1993. [2] T. Hibi, Algebraic Combinatorics on Convex Polytopes.Carslaw Publications, 1992. · Zbl 0772.52008
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