Question: Let F be a field and n a positive integer. Define R as the ring F[x]/(x), i.e., the quotient of the polynomial ring Fla] by

Let F be a field and n a positive integer. Define R as the ring F[x]/(x"), i.e., the quotient of the polynomial ring Fla] by the ideal generated by a".(5 points) Let f (:17) be a. polynomial in k[x] divisible by ac. Show that f (:17) = 0 in R

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

How we proceed f(1). Find a polynomial g(x) in Z[x] such that Ker d = (g(x)). Is there more than one possibility for g(x)? To what familiar ring is Z[x]/Ker o isomorphic? Do this exercise with Z...

. Let F be a field and define the ring F((x)) of formal Laurent series with coefficients from F by F((x)) =ax | an F and N Z). (Every element of F((x)) is a power series in x plus a polynomial in...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

re Regular Languages and Finite Automata (a) Let L be the set of all strings over the alphabet {a, b} that end in a and do not contain the substring bb. Describe a deterministic finite automaton...

Theeren ; "-x = TTI, (x) where fi (x)E (F. [ x] are the manic irreducible polynomials with dey (5, ) | n Proof Suppose flx) ElFLAJ is manic & irreducible & dog (f) In Then K' FPL x] / (food) is a...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

DETAILS What is the maximum segment length of a 100Base-FX netdwork, The last character ('X', etc) refers to the line code method used. Line code is a patdtern of voltage, current or photons used to...

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

answer all questions promptly What is the maximum segment length of a 100Base-FX netdwork,Thelast character('X', etc) refers to the line code method used. Line code is a pattern of voltage, current...

: (i) What data structures are maintained by the page manager. (ii) What happens when a machine performs a read operation to a page. (iii) What happens when a machine performs a write operation to a...

A taxpayer may avoid tax on income by having the payment made to another taxpayer. True False Caleb's medical expenses before reimbursement for 2021 include the following: Medical premiums $11,000...

Can the total overhead variance for a period be separated into price and efficiency variances? Explain.

To whom are accelerated death benefits payable? a . to the policy's insured b . to the policyowner c . to the policy's beneficiary d . to the policy's insured and beneficiary, equally

Classification model: Make a decision tree for the following: Pick a product that some in your group bought and others didn't. Label the top of the tree with the product description and the next...