A note on freeness
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914233681182720 |
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| author | Katzman, Mordechai |
| author_facet | Katzman, Mordechai |
| contents | In this brief note we show that for a field extension $K/F$, $S=K[\![\mathbf{x}]\!]$ is a free $R=F[\![\mathbf{x}]\!]$-module precisely when $K/F$ is finite. We then raise the question \emph{what is the projective dimension of $S$?} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on freeness Katzman, Mordechai Commutative Algebra 13A35, 13D07, 13J10, 13C10 In this brief note we show that for a field extension $K/F$, $S=K[\![\mathbf{x}]\!]$ is a free $R=F[\![\mathbf{x}]\!]$-module precisely when $K/F$ is finite. We then raise the question \emph{what is the projective dimension of $S$?} |
| title | A note on freeness |
| topic | Commutative Algebra 13A35, 13D07, 13J10, 13C10 |
| url | https://arxiv.org/abs/2512.16573 |