Ring theory question about polynomial rings

Let R={f(x) included in Q[x]: the coefficient of x in f(x) is 0} Prove that R is a subring of Q[x]. I know to prove a subring I need to show that there is a 1 in R (is this only to prove that it' a commutative subring with 1?), I know I also need to prove that R contains 2 elements that when subtracted are also in R, and I ...continues

Peter and Ray built a bike ramp

Peter and Ray built a bike ramp from 20 sheets of 4ft. X 8ft. plywood and propped it up on one end with some bricks. The finished ramp is rectangular. Show 3 ways they might have arranged the wood and give the measurment for each side. Assuming that they used every sheet of plywood, what is the total area of the ramp regardless ...continues

Text Book: - Contemporary Abstract Algebra, Author:- Gallien

In page 424 : - Theorem 25.1( Please mention each and every step). In page 424:- Theorem 25.2 (Please mention each and every step). Page 425 : - Theorem 25.3 (Please mention each and every step). Page 426 :- Corollary 1 and Corollary 2 (Please mention each and every step). In Page 430 (EXERCISE PROBLEMS). 1, 4, ...continues

Text Book: - Contemporary Abstract Algebra, Author:- Gallien

In page number 430 & 431 , I need following questions to be answered 6, 7, 8, 16 & 17. Last Question:- Give examples of groups with specific properties (Simple group & Non Simple Groups) At least 10 examples. (Please refer Chapter 25).? Please mention each and every step in an understandable manner.

Text Book:- Contemporary Abstract Algebra. Author:- Gallien

In page number 449, i need following questions to be answered: 4, 12/a, b, 21, 22, 24. 25. Please mention each and ever step.

Cayley Digraph

Please, can you graph this Cayley Digraph, like is in the attachment. I want you graph using Microsoft Word. Each dot is a vertex and the arrows are the edges. Please, do not confuse the vertex with the little 3 dots which means continuous the graph. If you have a question, let me know. I explain in attach you use two diff ...continues

Groups (Prove)

I need help with the following question : For a fixed element a of a group G, the set Ca ={ x element-of G|ax=xa} is the centralizer of a in G. Prove that for any a element-of G, Ca is a subgroup of G.

Groups - For a fixed positive integer n

** decide whether each of the given sets is a group with respect to the indicated operation. 1- For a fixed positive integer n, the set of all complex numbers x such that x^n=1(that is, the set of all nth roots of 1),with operation multiplication. 2-The set of all complex numbers x that have absolute value1, with operation ...continues

Groups - Suppose G is a finite group of even order. Show that there is at least one element a in G, a (is not equal to) e, such that a=a^-1

Prove the following : Suppose G is a finite group of even order. Show that there is at least one element a in G, a (is not equal to) e, such that a=a^-1

Quadratic Applications - Bicycle Shop

The manager of a bicycle shop has found that, a a price (in dollars) of p(x) = 150 - x/4 per bicycle, x bicycles will be sold. a.find an expression for the total revenue from the sale of x bicycles. b.find the number of bicycle sales that leads to maximum revenue. c.find the maximum revenue.