@ARTICLE{10.21494/ISTE.OP.2023.1000, 

TITLE={Some remarks on surjections of unit groups}, 
  
AUTHOR={Naseam Al-Kuleab, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={14}, 

NUMBER={Issue 4 (September 2023)}, 
	
YEAR={2023}, 

URL={http://openscience.fr/Some-remarks-on-surjections-of-unit-groups}, 
	
DOI={10.21494/ISTE.OP.2023.1000}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={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.}}