Natural Projection Homomorphisms Have Kernels That Are Easy to Find!

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In Ring Theory from Abstract Algebra, let R be a ring and let A be a (two-sided) ideal of R. The natural projection mapping π: R → R/A from the ring R to the factor ring (a.k.a. quotient ring) R/A is an onto homomorphism (we also say it is a surjection and an epimorphism). This function is defined by the formula π(r) = r + A, where r + A is the left coset of A in R containing r. What is the kernel of this natural mapping? It is the ideal A itself!

#AbstractAlgebra #RingTheory #homomorphism #FactorRing #QuotientRing

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  1. Bill Kinney
  2. abstract algebra
  3. ring theory
  4. group theory
  5. projection
  6. projection homomorphism
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