Abstract
Let $R$ be a ring. Following the literature, $R$ is called \textit {residually finite} if, for every $r\in R\backslash \{0\}$, there exists an ideal $I_r$ of $R$ such that $r\notin I_r$ and $R/I_r$ is finite. In this note, we define a \textit {strictly} infinite commutative ring $R$ with identity to be \textit {residually small} if, for every $r\in R\backslash \{0\}$, there exists an ideal $I_r$ of $R$ such that $r\notin I_r$ and $|R/I_r|\lt |R|$. The purpose of this article is to study such rings, extending results on (infinite) residually finite rings.
Citation
Greg Oman. Adam Salminen. "Residually small commutative rings." J. Commut. Algebra 10 (2) 187 - 211, 2018. https://doi.org/10.1216/JCA-2018-10-2-187
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