SOME PROPERTIES OF STAR OPERATIONS ON RING EXTENSIONS

Authors : Lokendra PAUDEL, Simplice TCHAMNA

Pages : 99-115

Doi:10.24330/ieja.969592

View : 17 | Download : 12

Publication Date : 2021-07-17

Article Type : Research Paper

Abstract :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 insert ignore into journalissuearticles values(P$\star$ME); if $insert ignore into journalissuearticles values(R_{[\m]}, \m _{[\m]});$ 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.
Keywords : Star operation, ring extension, Prüfer extension