Algebra retracts and Stanley–Reisner rings |
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Authors: | Neil Epstein Hop D Nguyen |
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Institution: | 1. Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, United States;2. Am Herrenberge 11, Appartment 419, 07745 Jena, Germany;3. Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genoa, Italy |
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Abstract: | In a paper from 2002, Bruns and Gubeladze conjectured that graded algebra retracts of polytopal algebras over a field k are again polytopal algebras. Motivated by this conjecture, we prove that graded algebra retracts of Stanley–Reisner rings over a field k are again Stanley–Reisner rings. Extending this result further, we give partial evidence for a conjecture saying that monomial quotients of standard graded polynomial rings over k descend along graded algebra retracts. |
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Keywords: | 13F55 13B99 14M25 05E40 |
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