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Mathematics > Commutative Algebra

arXiv:1301.3967 (math)
[Submitted on 17 Jan 2013 (v1), last revised 14 Dec 2013 (this version, v2)]

Title:Algebra retracts and Stanley-Reisner rings

Authors:Neil Epstein, Hop D. Nguyen
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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.
Comments: Incorporating several useful suggestions due to a referee. To appear in Journal of Pure and Applied Algebra
Subjects: Commutative Algebra (math.AC); Combinatorics (math.CO); Rings and Algebras (math.RA)
Cite as: arXiv:1301.3967 [math.AC]
  (or arXiv:1301.3967v2 [math.AC] for this version)
  https://doi.org/10.48550/arXiv.1301.3967
Journal reference: J. Pure Appl. Algebra 218 (2014), no. 9, 1665-1682
Related DOI: https://doi.org/10.1016/j.jpaa.2014.01.006

Submission history

From: Hop Nguyen [view email]
[v1] Thu, 17 Jan 2013 02:16:27 UTC (19 KB)
[v2] Sat, 14 Dec 2013 17:16:01 UTC (20 KB)
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