Algebra retracts and Stanley-Reisner rings
Commutative Algebra
2015-12-11 v2 Combinatorics
Rings and Algebras
Abstract
In a paper from 2002, Bruns and Gubeladze conjectured that graded algebra retracts of polytopal algebras over a field are again polytopal algebras. Motivated by this conjecture, we prove that graded algebra retracts of Stanley-Reisner rings over a field 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 descend along graded algebra retracts.
Cite
@article{arxiv.1301.3967,
title = {Algebra retracts and Stanley-Reisner rings},
author = {Neil Epstein and Hop D. Nguyen},
journal= {arXiv preprint arXiv:1301.3967},
year = {2015}
}
Comments
Incorporating several useful suggestions due to a referee. To appear in Journal of Pure and Applied Algebra