Homomorphism between Rings

Authors

  • Vinod S. Department of Mathematics, Government College for Women (University of Kerala), Thiruvananthapuram, Kerala
  • Biju G. S. Department of Mathematics, College of Engineering (Kerala Technological University), Thiruvananthapuram 695016, Kerala
  • Minikumari N. S. Department of Mathematics, College of Engineering (Kerala Technological University), Thiruvananthapuram 695016, Kerala

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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H. Kestelman, Automorphisms of the field of complex numbers, Proceedings of the London Mathematical Society 2(1) (1951), 1 – 12, DOI: 10.1112/plms/s2-53.1.1.

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

30-09-2020
CITATION

How to Cite

S., V., G. S., B., & N. S., M. (2020). Homomorphism between Rings. Communications in Mathematics and Applications, 11(3), 481–487. https://doi.org/10.26713/cma.v11i3.1415

Issue

Section

Research Article