TY  - Type of reference 
TI  - Some remarks on surjections of unit groups 
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  - Advances in Pure and Applied Mathematics 
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  - http://openscience.fr/IMG/pdf/iste_apam23v14n4_3.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2023/09/8 
SN  - 1869-6090 
TT  - Remarques sur les surjections des groupes unitaires 
UR  - http://openscience.fr/Some-remarks-on-surjections-of-unit-groups 
IS  - Issue 4 (September 2023) 
VL  - 14 
ER  -