If S is a subring of a ring R, then S[a] is a subring of R[x]. Exercise 2.35.1 Prove this assertion! In particular, this shows that Q[x] is a subring of R[r], which in turn is a subring of C[r].

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 16E: A Boolean ring is a ring in which all elements x satisfy x2=x. Prove that every Boolean ring has...
icon
Related questions
Question

abstract algebra

Example 2.35
If S is a subring of a ring R, then Sr] is a subring of Rr].
Exercise 2.35.1
Prove this assertion!
In particular, this shows that Q[x] is a subring of R[x], which in turn is
a subring of C[x].
Transcribed Image Text:Example 2.35 If S is a subring of a ring R, then Sr] is a subring of Rr]. Exercise 2.35.1 Prove this assertion! In particular, this shows that Q[x] is a subring of R[x], which in turn is a subring of C[x].
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,