Finding the relation between ring and mod integers
Not what you're looking for?
R is the set of integers mod 7 under the addition and multiplication mod 7.
That is, the elements of R are the seven symbols 0^,1^,2^,3^,4^,5^,6^
where
(1) I^+j^=k^ where k is the remainder of I + j on division by 7
(thus for instance, 4^+5^=2^ since 4 + 5 = 9 , which when divided by 7
leaves remainder of 2)
(2) i^, j^ = m^ where m is the remainder of ij on division by. 7
(thus , 5^°3^ = 1^ since..5.3 =15 has 1 as remainder on the division by 7)
Prove that R is a commutative ring with unit element.
The complete problem is in the attached file.
Purchase this Solution
Solution Summary
The Solution proves that R, the set of integers mod 7 under the addition and multiplication mod 7 is a commutative ring with unit element.
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
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.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Probability Quiz
Some questions on probability