Question

Please, help me with a very detailed and self-explanatory solution to this problem. I will appreciate it alot. Thank you

Step 1

Problem concerns the ring and vector space structure of the space of formal power series over K, K a field

Step 2

(a) Here K[x] is the ring of polynomials over K ; note that any polynomial consisists only finitely many terms . Thus , as a vector space ,K[x] is isomorphic to the space of sequences over K which are eventually 0, (as described in the last two lines

Step 3

(a) in contrast, K<<x>> is the ring of formal power series , here an element of K<<x>> can have infinitely many non-zero coefficients....

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Sorry about that. What wasn’t helpful?