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arXiv · 2410.17007

On the transfer of certain ring-theoretic properties in Anderson rings

Hyungtae Baek·Jung Wook Lim·Ali Tamoussit
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Abstract

Let $R$ be a commutative ring with unity and let $X$ be an indeterminate over $R$. The \textit{Anderson ring} of $R$ is defined as the quotient ring of the polynomial ring $R[X]$ by the set of polynomials that evaluate to $1$ at $0$. Specifically, the Anderson ring of $R$ is $R[X]_A$, where $A=\{f\in R[X]\mid f(0)=1\}$. In this paper, we aim to investigate the transfer of various ring-theoretic properties between the ring $R$ and its Anderson ring $R[X]_A$. Interesting results are established, accompanied by applications and illustrative examples.

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Hyungtae Baek, Jung Wook Lim, Ali Tamoussit. 2024-10-22. On the transfer of certain ring-theoretic properties in Anderson rings. https://arxiv.org/abs/2410.17007

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