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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.14382 |
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| _version_ | 1866909585852334080 |
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| author | Chakraborty, Sagnik Pal, Madhuparna |
| author_facet | Chakraborty, Sagnik Pal, Madhuparna |
| contents | Let $R$ be a ring and $B = R[X_1, \dots, X_n]$ the polynomial ring in $n$ variables over $R$. In this article, we consider retractions $φ: B \longrightarrow B$ such that $φ(X_i)$ is either a monic monomial or $0$. We prove that if $R$ is an integral domain, then any such retract is isomorphic to $R^{[p]}$, the polynomial ring in $p$ variables over $R$, for some $0 \le p \le n$. We also characterize different monomial retractions of $B$ which give the same retract. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monomial retracts of polynomial rings are polynomial rings Chakraborty, Sagnik Pal, Madhuparna Commutative Algebra 13B25, 14A05 Let $R$ be a ring and $B = R[X_1, \dots, X_n]$ the polynomial ring in $n$ variables over $R$. In this article, we consider retractions $φ: B \longrightarrow B$ such that $φ(X_i)$ is either a monic monomial or $0$. We prove that if $R$ is an integral domain, then any such retract is isomorphic to $R^{[p]}$, the polynomial ring in $p$ variables over $R$, for some $0 \le p \le n$. We also characterize different monomial retractions of $B$ which give the same retract. |
| title | Monomial retracts of polynomial rings are polynomial rings |
| topic | Commutative Algebra 13B25, 14A05 |
| url | https://arxiv.org/abs/2504.14382 |