Purchase Solution

# Commutative rings and Nilpotent Elements

Not what you're looking for?

Let R be a commutative ring with 1 not equal to zero. Prove that if "a" is a nilpotent element of R then 1-ab is a unit for all "b" in R.

##### Solution Summary

Commutative rings and nilpotent elements are investigated.

##### Solution Preview

since a is nilpotent, there is a positive integer n such that a^n = 0

observe that, in particular if ...

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Probability Quiz

Some questions on probability

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.