$R$-CONVEX SUBSETS OF BIMODULES OVER $*$-RINGS | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 1، آذر 2024، صفحه 91-103 اصل مقاله (150.88 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11817.1605 | ||
| نویسندگان | ||
| Ismail Nikoufar* 1؛ Ali Ebrahimi Meymand2 | ||
| 1Department of Mathematics, Payame Noor University, Tehran, Iran. | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. | ||
| 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 $f$-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. | ||
| کلیدواژهها | ||
| $R$-convex sets؛ $R$-extreme points؛ $f$-homomorphism | ||
| مراجع | ||
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