In Ring Theory from Abstract Algebra, if R is a ring and A is an ideal of R, then the natural projection mapping π: R → R/A (from R to the factor ring (quotient ring) R/A) defined by π(r) = r + A is a ring homomorphism with kernel Ker(π) = A. It is easy to prove this using the definition of factor ring addition and multiplication as well as a coset equaling the ideal if and only if the coset representative is in the ideal. 🔴 "Contemporary Abstract Algebra", by Joe Gallian: [ Ссылка ]

🔴 Abstract Algebra Exam 1 Review Problems and Solutions: [ Ссылка ]

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