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PreprintarXiv licencearXiv

Cube-freeness and a square formula for canonical trace ideals of Stanley--Reisner rings

  • Sora Miyashita
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Abstract

Let I be a monomial ideal in S=k[x1,…,xn], and set R=S/I. We prove that if I is a-bounded and M is a positively b-determined R-module, then trR(M) is (a+b)-bounded. For the canonical module, this gives the bound 2a. In particular, the canonical trace ideal of every Stanley--Reisner ring is a cube-free monomial ideal. We also prove that, for a Stanley--Reisner ring satisfying (S2), the canonical trace ideal is the square of its radical if and only if the ring satisfies (G2).

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Cite

BibTeXRIS
BibTeX
@misc{miyashita2026cubefreeness,
  title = {{Cube-freeness and a square formula for canonical trace ideals of Stanley--Reisner rings}},
  author = {Sora Miyashita},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00714},
  eprint = {2611.00714},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00714},
}
RIS
TY  - UNPB
TI  - Cube-freeness and a square formula for canonical trace ideals of Stanley--Reisner rings
AU  - Sora Miyashita
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00714
UR  - https://arxiv.org/abs/2611.00714
AB  - Let I be a monomial ideal in S=k[x_1,…,x_n], and set R=S/I. We prove that if I is a-bounded and M is a positively b-determined R-module, then tr_R(M) is (a+b)-bounded. For the canonical module, this gives the bound 2a. In particular, the canonical trace ideal of every Stanley--Reisner ring is a cube-free monomial ideal. We also prove that, for a Stanley--Reisner ring satisfying (S_2), the canonical trace ideal is the square of its radical if and only if the ring satisfies (G_2).
ER  -