Let f = ao+ajx+…+a„x" be a polynomial. I can treat f as an element of R[x] by defining an+1,&n+2,... all to equal 0. This shows that R[] CR[x]. If you had already proved that R[x] was a ring, how could you use this fact to help you prove R[x] is a ring?
Let f = ao+ajx+…+a„x" be a polynomial. I can treat f as an element of R[x] by defining an+1,&n+2,... all to equal 0. This shows that R[] CR[x]. If you had already proved that R[x] was a ring, how could you use this fact to help you prove R[x] is a ring?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let f = ao+ajx+…+a„x" be a polynomial. I can treat f as an element of R[x]
by defining an+1,&n+2,... all to equal 0. This shows that R[] CR[x].
If you had already proved that R[x] was a ring, how could you use this fact to
help you prove R[x] is a ring?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc33fa3ef-6a6a-465a-986f-fdde28dde808%2F663612d9-c7e1-454b-bed5-48bc278f898e%2Foqy5y2c_processed.png&w=3840&q=75)
Transcribed Image Text:Let f = ao+ajx+…+a„x" be a polynomial. I can treat f as an element of R[x]
by defining an+1,&n+2,... all to equal 0. This shows that R[] CR[x].
If you had already proved that R[x] was a ring, how could you use this fact to
help you prove R[x] is a ring?
![Let IR[:] be the set of all expressions
a = ao +ajx+azx² + ……=
i=0
where a; E R for all nonnegative integers i. Informally, an element of R[x] is like a
polynomial except that it can have infinitely many terms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc33fa3ef-6a6a-465a-986f-fdde28dde808%2F663612d9-c7e1-454b-bed5-48bc278f898e%2Fzo80zed_processed.png&w=3840&q=75)
Transcribed Image Text:Let IR[:] be the set of all expressions
a = ao +ajx+azx² + ……=
i=0
where a; E R for all nonnegative integers i. Informally, an element of R[x] is like a
polynomial except that it can have infinitely many terms.
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