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I am reading Paul E. Bland's book, "The Basics of Abstract Algebra".
I am currently focused on Chapter 6: Polynomial Rings.
I need help with an aspect of Theorem 6.3.17.
Theorem 6.3.17 requires awareness of the notation of Definition 6.3.15 which reads as follows:
https://www.physicsforums.com/attachments/4690Theorem 6.3.17 reads as follows:https://www.physicsforums.com/attachments/4691In the above Theorem we read the following:" ... ... and it is not difficult to show that
$$[f]_p (x) = [g]_p (x) [h]_p (x)$$ ... ... "Although it seems plausible that $$[f]_p (x) = [g]_p (x) [h]_p (x)$$, I am unable to rigorously demonstrate that this is the case.
Can someone help me to prove that $$[f]_p (x) = [g]_p (x) [h]_p (x)$$?
Hope someone can help ... ...
Peter
I am currently focused on Chapter 6: Polynomial Rings.
I need help with an aspect of Theorem 6.3.17.
Theorem 6.3.17 requires awareness of the notation of Definition 6.3.15 which reads as follows:
https://www.physicsforums.com/attachments/4690Theorem 6.3.17 reads as follows:https://www.physicsforums.com/attachments/4691In the above Theorem we read the following:" ... ... and it is not difficult to show that
$$[f]_p (x) = [g]_p (x) [h]_p (x)$$ ... ... "Although it seems plausible that $$[f]_p (x) = [g]_p (x) [h]_p (x)$$, I am unable to rigorously demonstrate that this is the case.
Can someone help me to prove that $$[f]_p (x) = [g]_p (x) [h]_p (x)$$?
Hope someone can help ... ...
Peter