Photo by emileseguin from unsplash
It is shown that every dp-minimal integral domain $R$ is a local ring and for every non-maximal prime ideal $\mathfrak p $ of $R$, the localization $R_{\mathfrak p }$ is… Click to show full abstract
It is shown that every dp-minimal integral domain $R$ is a local ring and for every non-maximal prime ideal $\mathfrak p $ of $R$, the localization $R_{\mathfrak p }$ is a valuation ring and $\mathfrak{p}R_{\mathfrak{p}}=\mathfrak{p}$. Furthermore, a dp-minimal integral domain is a valuation ring if and only if its residue field is infinite or its residue field is finite and its maximal ideal is principal.
Keywords:
minimal integral;
integral domains;
mathfrak
Journal Title: Israel Journal of Mathematics
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Israel Journal of Mathematics
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!