Purchase Solution

Ideals : Cyclic Module in a Commutative Ring

Not what you're looking for?

Ask Custom Question

Prove that every cyclic module in a commutative ring R is of the form R/L for some ideal L. //Note: R/L is said "R modulo L."

Purchase this Solution

Solution Summary

Ideals and a cyclic module in a commutative ring are investigated and discussed in the solution. The solution is detailed and well presented.

Solution Preview

Prove that every cyclic module in a commutative ring R is of the form R/L for some ideal L. //Note: R/L is said "R modulo L"

***************************************************************

Definitions (from Fraleigh)

-- Let R be a ring. A (left) R-module consists of an abelian group M together with an operation of external multiplication of each element of M by each element of R on the left such that for all a, b elements of M and r,s elements of R,
(1) ra is an element of M, (2) r(a + b) = ra + rb, (3) (r + s)a = ra + sa, (4) (rs)a = r(sa)

(It is *not* necessary for M to be a subset of R, but in the ...

Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

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.

Solving quadratic inequalities

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

Multiplying Complex Numbers

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