Graded Injective Domains

Mike Hensler; Hannah Klawa

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arXiv · 2505.16143

Graded Injective Domains

Mike Hensler·Hannah Klawa

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Abstract

An integral domain $R$ is an $i$-domain if for every overring $S$ of $R$, $\text{Spec}(S) \rightarrow \text{Spec}(R)$ is injective and is a mated integral if for every overring $S$ of $R$ and prime ideal $P$ of $R$ such that $PS \neq S$, there exists exactly one prime ideal $Q$ of $S$ such that $Q \cap R = P$. In this paper, we explore graded notions of $i$-domains and mated domains and their connection with gr-Pr\"{u}fer domains.

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Mike Hensler, Hannah Klawa. 2025-05-22. Graded Injective Domains. https://arxiv.org/abs/2505.16143

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