On Lengths of $\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)$
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916362201333760 |
|---|---|
| author | Han, Fiona Kenkel, Jennifer Li, Daniel Venkatesh, Sridhar Wiles, Ashley |
| author_facet | Han, Fiona Kenkel, Jennifer Li, Daniel Venkatesh, Sridhar Wiles, Ashley |
| contents | In this paper, we provide a formula for the vector space dimension of the ring $\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)$ over $\mathbb{F}_2$ when $d_1,d_2,d_3$ all lie between successive powers of $2$. For general $d_1,d_2,d_3$, we provide a simple algorithm to calculate the vector space dimension of $\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)$ by combining our formula with certain results of Chungsim Han (1992). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16574 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Lengths of $\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)$ Han, Fiona Kenkel, Jennifer Li, Daniel Venkatesh, Sridhar Wiles, Ashley Commutative Algebra In this paper, we provide a formula for the vector space dimension of the ring $\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)$ over $\mathbb{F}_2$ when $d_1,d_2,d_3$ all lie between successive powers of $2$. For general $d_1,d_2,d_3$, we provide a simple algorithm to calculate the vector space dimension of $\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)$ by combining our formula with certain results of Chungsim Han (1992). |
| title | On Lengths of $\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)$ |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2306.16574 |