Purchase Solution

Finitely Generated Z-modules

Not what you're looking for?

Ask Custom Question

Definition: Let R be a commutative ring with identity, let M be an R-module, and let B be a nonempty subset of M. Then the set RB is defined as

RB is a submodule. If B is a finite set, say , we write for RB, and say that RB is a finitely generated R-module. In particular, if for some , we say that M is finitely generated, and that is a generating set for M.

Exercise: Show that the and are finitely generated, by giving a finite generating set for each. Where Z stands for the integers.

Please see the attached file for the fully formatted problems.

Attachments
Purchase this Solution

Solution Summary

Finitely Generated Z-modules are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Definition: Let R be a commutative ring with identity, let M be an R-module, and let B be a nonempty subset of M. Then the set RB is defined as

RB is a ...

Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

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

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.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.