$R$-CONVEX SUBSETS OF BIMODULES OVER $*$-RINGS

نویسندگان

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.

doi
10.22044/jas.2022.11817.1605
چکیده

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 $f$-homomorphismfrom $M$ to $N$ carries $R$-convex subsets and its $R$-extreme points to $B$-convex subsets and its $B$-extreme pointsand vice versa.\linebreak Moreover, we confirm that the $R$-convex hull of invariant subsets under $f$-homomorphismsremains invariant.