Improved Bounds for the s-multiplicity
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908657572118528 |
|---|---|
| author | Liu, Zhongkui Qin, Junquan Yang, Xiaoyan |
| author_facet | Liu, Zhongkui Qin, Junquan Yang, Xiaoyan |
| contents | Let (RmR), (SmS) and (TmT) be Noetherian local rings sharing the same
residue eld k and prime characteristic p > 0. We establish some formulas relating the
h-function and s-multiplicity of the ber product R T S in terms of the h-functions and
s-multiplicities of R, T and S. Furthermore, we derive formulas that connect the h-function
and s-multiplicity of the idealization ring R M to the corresponding invariants of R and M,
where M is a nitely generated R-module. As applications of these results, we derive new
estimates for the Taylor-Miller question and the Watanabe-Yoshida conjecture concerning
s-multiplicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved Bounds for the s-multiplicity Liu, Zhongkui Qin, Junquan Yang, Xiaoyan Commutative Algebra 13D40, 13H15, 13H05 Let (RmR), (SmS) and (TmT) be Noetherian local rings sharing the same residue eld k and prime characteristic p > 0. We establish some formulas relating the h-function and s-multiplicity of the ber product R T S in terms of the h-functions and s-multiplicities of R, T and S. Furthermore, we derive formulas that connect the h-function and s-multiplicity of the idealization ring R M to the corresponding invariants of R and M, where M is a nitely generated R-module. As applications of these results, we derive new estimates for the Taylor-Miller question and the Watanabe-Yoshida conjecture concerning s-multiplicity. |
| title | Improved Bounds for the s-multiplicity |
| topic | Commutative Algebra 13D40, 13H15, 13H05 |
| url | https://arxiv.org/abs/2511.12946 |