TY - Type of reference TI - Remarques sur les surjections des groupes unitaires AU - Naseam Al-Kuleab AB - The main purpose of this paper is to study unital ring homomorphisms of associative rings $$$\varphi : R\rightarrow S$$$ satisfying one of the following conditions : (a) the unit-preserving property : $$$\varphi(R^{\times})=S^{\times}$$$ and (b) the inverse unit-preserving property : $$$\varphi^{-1}(S^{\times})=R^{\times}$$$. We establish the relationship between these two conditions. Several characterizations of such conditions are settled. An application to the index of unit groups of rings $$$R\subset S$$$ having a nonzero common ideal is given. DO - 10.21494/ISTE.OP.2023.1000 JF - Avancées en Mathématiques Pures et Appliquées KW - Associative ring, ideal, group of units, left Artinian, von Neumann regular, Jacobson radical, Associative ring, ideal, group of units, left Artinian, von Neumann regular, Jacobson radical, L1 - https://www.openscience.fr/IMG/pdf/iste_apam23v14n4_3.pdf LA - fr PB - ISTE OpenScience DA - 2023/09/8 SN - 1869-6090 TT - Some remarks on surjections of unit groups UR - https://www.openscience.fr/Remarques-sur-les-surjections-des-groupes-unitaires IS - Numéro 4 (Septembre 2023) VL - 14 ER -