Let R be a commutative ring and let A be an ideal of R. Show that VA = {x e R:x" e A for some positive integer n} is an ideal of R such that (i) AS VĀ (iii) If R has unity and VA = R, then A = R. (ii) VWA = VA %3D
Let R be a commutative ring and let A be an ideal of R. Show that VA = {x e R:x" e A for some positive integer n} is an ideal of R such that (i) AS VĀ (iii) If R has unity and VA = R, then A = R. (ii) VWA = VA %3D
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.1: Ideals And Quotient Rings
Problem 24E: 24. If is a commutative ring and is a fixed element of prove that the setis an ideal of . (The set...
Related questions
Question
All subparts
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,