Algebra retracts and Stanley-Reisner rings

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.

Incorporating several useful suggestions due to a referee. To appear in Journal of Pure and Applied Algebra

References in corpus (1)

• A Counter-example to the Cancellation Problem for the Affine Space A^3 in characteristic p

Cited by in corpus (4)

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• Ascent and descent of the Golod property along algebra retracts
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