SOME PROPERTIES OF STAR OPERATIONS ON RING EXTENSIONS

Year 2021, , 99 - 115, 17.07.2021

Lokendra Paudel Simplice Tchamna

https://doi.org/10.24330/ieja.969592

Cited By: 2

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 (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.

Keywords

Star operation, ring extension, Prüfer extension

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