Titre : Some remarks on surjections of unit groups 

Auteurs : Naseam Al-Kuleab,  

Revue : Advances in Pure and Applied Mathematics 

Numéro : Issue 4 (September 2023) 

Volume : 14 

Date : 2023/09/8 

DOI : 10.21494/ISTE.OP.2023.1000 

ISSN : 1869-6090 

Résumé : 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. 

Éditeur : ISTE OpenScience