You are here:

Advanced Math/Abstract Algebra

Advertisement

Expert: Sherry Wallin - 10/28/2010


Question
Dear Sherry Wallin,

I was given a question as below which I do not understand what does it mean and need your help to enlighten.

Let R = Z2[x]/<x^3 + x^2 + 1>.
(b) Does there exist an element a belongs R such that a, a^2, a^3, a^4, . . . , a^8 give all the nonzero elements of R? Justify your answer.

Answer
Raymond I need to know if your notation is saying the quotient group
Z2[x]/<x^3 + x^2 + 1>? Then you are looking for all the factors in base 2 of the polynomial x^3 + x^2 + 1. And then you want to raise each factor to each power (1,2,...,8) and see it generates all the elements. Please clarify.

Math Prof

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

©2012 About.com, a part of The New York Times Company. All rights reserved.