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 Zn to Zm and from Qn to Qm. Also, we characterize and compute all continuous ring homomorphism from Rn to R.

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References

A. Cameron, Counting ring homomorphisms, Pi Mu Epsilon Journal 13(2) (2010), 65 – 67, DOI: https://www.jstor.org/stable/24340801?seq=1.

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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.

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

Vol. 11 No. 3 (2020)

Section

Research Article

License

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