# Three Algebra Problems with Groups, Isomorphism, and Automorphism

Subject Mathematics Abstract Algebra

## Question

See the below file.

## Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

1. We assume by contradiction that (R, +) ~ (R*, x).
Then neutral element from the left side must be mapped to neutral element from the right side.
This means f(0, +)=f(1,x) (0 is the neutral element for (R,+) and 1 is the neutral element for (R*,x).
Also, since the two are isomorphic => f is bijection => f is both one-to-one and onto....

This is only a preview of the solution. Please use the purchase button to see the entire solution

## Related Homework Solutions

Abstract Algebra Questions
\$60.00
Abstract Algebra
Commutative Property
Associative Property
Multiplication
Fields
Rings
Subsets
Functions
Composition
Multiplication
Binary Operations
Subfields
Contemporary Abstract Algebra
\$65.00
Contemporary
Abstract
Algebra
Mathematics
Subgroup
Divisor
Cyclic
Group
Elements
Homomorphism
Contemporary Abstract Algebra
\$40.00
Contemporary
Abstract
Algebra
Mathematics
Distinct
Logical
Explanation
Prime
Non- Abelian
Theorem
Linear Congruence Problem
\$10.00
Linear
Congruence
GCD
Equation
Integer
Euclidean
Combination
Unique
Solution
Algorithm
Abstract Algebra Questions
\$40.00
Abstract Algebra
Homomorphism
Kernel
Functions
Theorems
Elements
Abelian Groups
Polynomials
Diagram
Isomorphism
Permutation
Transpositions
Factorization Questions
\$40.00
Factorization
Polynomial
Mathematics
Abstract Algebra
Irreducibility
PID
UFD
Live Chats