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Homomorphisms and Ideals

  • Joseph Rotman
Part of the Universitext book series (UTX)

Abstract

If R and S are rings, then a function ψ: RS is a ring homomorphism (or ring map) if, for all r, r′, 1 ∈ R:
$$ \psi \left( {r + r'} \right) = \psi (r) + \psi \left( {r'} \right) $$
$$ \psi \left( {rr'} \right) = \psi (r)\psi \left( {r'} \right) $$
$$ \psi (1) = 1 $$
A ring homomorphism ψ: RS is an isomorphism if ψ is a bijection;1 in this case, one says that R and S are isomorphic and one writes RS.

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Joseph Rotman
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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