Let $\star$ be a star operation on a ring extension $R\subseteq S$. A ring extension $R\subseteq S$ is called
Pr\"ufer $star$-multiplication extension (P$\star$ME) if $(R_{[\m]}, \m _{[\m]})$ is a Manis pair in $S$ for
every $\star$-maximal ideal $\m$ of $R$. We establish some results on star operations, and we study P$\star$ME
in pullback diagrams of type $\square$. We show that, for a
maximal ideal $\m$ of $R$, the extension $R_{[\m]} \subseteq S$ is
Manis if and only if $R[X]_{[\m R[X]]} \subseteq S[X]$ is a Manis
extension.
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 17 Temmuz 2021 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 30 Sayı: 30 |