Document Type : Original Manuscript


1 Department of Mathematics, Payame Noor University, Tehran, Iran.

2 Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.


Let $M$ and $N$ be bimodules over the unital $*$-rings $R$ and $B$, respectively.
We investigate the notion of $R$-convexity and the corresponding notion of $R$-extreme points.
We discuss the effect of an $f$-homomorphism on
$R$-convex subsets and its\linebreak $R$-extreme points.
Namely, we declare how an $f$-homomorphism
from $M$ to $N$ carries $R$-convex subsets and its $R$-extreme points to $B$-convex subsets and its $B$-extreme points
and vice versa.\linebreak Moreover, we confirm that the $R$-convex hull of invariant subsets under $f$-homomorphisms
remains invariant.


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