Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

RING HOMOMORPHISMS BETWEEN MAXIMAL SUBRINGS OF REAL NUMBERS

Document Type : Original Paper

Author
Alborz Azarang
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
10.22055/jamm.2025.50224.2392
Abstract
We prove that if $S$ is a local radically closed subring of $\mathbb{R}$, then each ring homomorphism from $S$ to $\mathbb{R}$ is the inclusion map. In particular, if $S_1$ and $S_2$ are maximal subrings of $\mathbb{R}$, then there exists a ring homomorphism $\phi:S_1\rightarrow S_2$ if and only if $S_1=S_2$ and in this case $\phi$ is the identity.
Keywords
Ring homomorphism
local ring
integrally closed
maximal subring
Subjects
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  • Receive Date 20 July 2025
  • Revise Date 30 October 2025
  • Accept Date 23 December 2025