Purchase Solution

Subring R of integral domain D is a subdomain of D.

Not what you're looking for?

Ask Custom Question

Modern Algebra
Ring Theory
Subrings
Integral Domain

1) If D is an integral domain and R< = D is a subring of D with unity, show that R is a subdomain of D.
This amounts to showing that 1subR and 1subD are unities from R and D respectively

2) Give an example with D not integral domain where 1subR =/= 1 sub D
(Hint: consider Rsub1 X Rsub2. Warning Rsub1 is not a subring of Rsub1 X Rsub2; it's not even a subset of it)

Note : R <= D means R is a subring of D
1subR means 1 is element of R
1subD means 1 is element of D
Rsub1 mean that R subscrip1
Rsub1 X Rsub2 means cross product.

Purchase this Solution

Solution Summary

This solution is comprised of a detailed explanation that subring R of integral domain D is a subdomain of D.

Solution Preview

Modern Algebra
Ring Theory
Subrings
Integral Domain

1) If D ...

Solution provided by:
Education
  • BSc, Manipur University
  • MSc, Kanpur University
Recent Feedback
  • "Thanks this really helped."
  • "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
  • "Very nice thank you"
  • "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
  • "You are awesome. Thank you"
Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

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

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.

Graphs and Functions

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

Solving quadratic inequalities

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