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Jung Wook Lim

Publications and source records attributed to Jung Wook Lim.

5 recordsLinked to original sources
arXiv2026

Local properties of integral domains under extensions and pullback constructions

For a property $\mathcal{X}$ of integral domains, an integral domain $D$ is said to be a {\it locally $\mathcal{X}$-domain} if $D_P$ has the property $\mathcal{X}$ for every prime ideal $P$ of $D$. In this paper, we study the transfer of local properties of integral domains under several extensions and constructions, including flat overrings, Nagata ideal transforms, polynomial rings and their quotient extensions, and pullback constructions.

math.AC↗
arXiv2026

A special subring of the Nagata ring and the Serre's conjecture ring

Many ring theorists researched various properties of Nagata rings and Serre's conjecture rings. In this paper, we introduce a subring (refer to the Anderson ring) of both the Nagata ring and the Serre's conjecture ring (up to isomorphism), and investigate properties of the Anderson ring. Additionally, we compare the properties of the Anderson ring with those of the Nagata ring and the Serre's conjecture ring.

math.AC↗
arXiv2025

On $S$-$n$-absorbing ideals

Let $R$ be a commutative ring with identity, $S$ a multiplicative subset of $R$ and $I$ an ideal of $R$ disjoint from $S$. In this paper, we introduce the notion of an $S$-$n$-absorbing ideal which is a generalization of both the $S$-prime ideals and $n$-absorbing ideals. Moreover, we investigate the basic properties, quotient extension, existence and amalgamation of $S$-$n$-absorbing ideals.

math.AC↗
arXiv2024

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

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.

math.AC↗