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 - https://www.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 - https://www.openscience.fr/Some-remarks-on-surjections-of-unit-groups
IS - Issue 4 (September 2023)
VL - 14
ER -