arXiv subjects

Hannah Klawa

Publications and source records attributed to Hannah Klawa.

4 recordsLinked to original sources

arXiv2025

Gen AI in Proof-based Math Courses: A Pilot Study

With the rapid rise of generative AI in higher education, understanding how students use AI is increasingly important. This exploratory study examines student use and perceptions of generative AI across three proof-based undergraduate mathematics courses: a first-semester abstract algebra course, a topology course, and a second-semester abstract algebra course. In each case, course policy permitted some use of generative AI. Drawing on survey responses and student interviews, we analyze how students engaged with AI tools as well as their perceptions of generative AI's usefulness, accuracy and limitations.

cs.AI↗

arXiv2025

Graded Injective Domains

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-Prüfer domains.

math.AC↗

arXiv2023

Graded Perinormality

An integral domain $R$ is \emph{perinormal} if every local going-down overring is a localization of $R$ and \emph{globally perinormal} if every going-down overring is a localization of $R$. In this paper, I introduce notions of graded perinormal and graded globally perinormal domains and show that many results obtained for perinormal and globally perinormal domains have graded analogs. I also give some results for descent of properties between a graded domain and its $0$th graded component.

math.AC↗

arXiv2023

Global perinormality in a generalized $D + M$ construction

A domain $R$ is \emph{perinormal} if every going-down overring is flat and a perinormal domain $R$ is \emph{globally perinormal} if every flat overring is a localization of $R$ [Epstein-Shapiro 2016]. I show that global perinormality is preserved in a pullback construction which encompasses a classical $D+M$ construction. In doing so, a result is given for the transfer of the property that every flat overring is a localization in the pullback construction considered.

math.AC↗