- #1

RJLiberator

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## Homework Statement

Let F(ℝ) = {ƒ:ℝ->ℝ}

define (f+g)(x) = f(x)+g(x)

(f*g)(x) = f(x)*g(x)

F(ℝ) is a commutative ring.

ƒ_0(x) = 0 and ƒ_1(x) = 1

a) Describe all units and zero divisors

b) Find a function f such that ƒ≠ƒ_0, ƒ≠ƒ_1, and ƒ^2 = ƒ

## Homework Equations

A

**unit**is an element r ∈ R, which has a multiplicative inverse s∈R with r*s = 1.

A

**zero divisor**is an element r ∈R such that there exists s∈R and rs = 0 (or sr=0).

## The Attempt at a Solution

This is a review problem for my upcoming abstract algebra exam. The professor stated that this or the other problem he gave us, will be on the exam.

So I want to get this one down.

a) The definitions of units and zero divisors are obvious, but the way the problem is stated makes it difficult to understand.

So in this initial statement, the problem is saying that functions from ℝ sent to ℝ ?

Would the units be all functions such that ƒ_1(x) = 1 ? I mean, I guess I need to go into more detail then this, correct?

Are there any examples someone can give me of what the problem actually is saying?

The problem will likely be easy for me to solve if I know this element of it as I understand what the questions are asking / definitions.