9.18. Let Ij C I2 C I3 C …… be ideals of R. Let I = U, In. 1. Show that I is an ideal of R. 2. Suppose that R/I is commutative. Show that for every a, b e R, there exists an n e N such that ab – ba e In.
9.18. Let Ij C I2 C I3 C …… be ideals of R. Let I = U, In. 1. Show that I is an ideal of R. 2. Suppose that R/I is commutative. Show that for every a, b e R, there exists an n e N such that ab – ba e In.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 22E: Let ab in a field F. Show that x+a and x+b are relatively prime in F[x].
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Could you explain how to show 9.18 in detail? I included list of theorems and definitions from the textbook.
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