# Homomorphism between Rings

## DOI:

https://doi.org/10.26713/cma.v11i3.1415## Keywords:

Homomorphism, Rings, Continuous function## Abstract

In this paper, using elementary algebra and analysis, we characterize and compute all ring homomorphism from \(\mathbb{Z}^n\) to \(\mathbb{Z}^m\) and from \(\mathbb{Q}^n\) to \(\mathbb{Q}^m\). Also, we characterize and compute all continuous ring homomorphism from \(\mathbb{R}^n\) to \(\mathbb{R}\).

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## References

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J. A. Gallian and D. S. Jungreis, Homomorphisms from (Z_m[i]) into (Z_n[i]) and (Zm[rho]) into (Z_n[rho]), where (i^2+1=0) and (rho^2+rho+1=0), The American Mathematical Monthly 95(3) (1988), 247 – 249, DOI: 10.1080/00029890.1988.11971992.

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M. Saleh and H. Yousef, The number of ring homomorphisms from (Z_{m_1}times Z_{m_2}times cdots Z_{m_r}) to (Z_{k_1}times Z_{k_2}times cdots times Z_{k_s}), The American Mathematical Monthly 105(3) (1998), 259 – 260, DOI: 10.1080/00029890.1998.12004878.

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## Published

## How to Cite

*Communications in Mathematics and Applications*,

*11*(3), 481–487. https://doi.org/10.26713/cma.v11i3.1415

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