Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math

College Archive

_____________________________________________
Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ
_____________________________________________

TOPICS
space
This page:
  modern algebra checkmark

  Search
  Dr. Math

See also the
Internet Library:
  modern algebra



COLLEGE

Algorithms
Analysis
Algebra
   linear algebra
   modern algebra

Calculus
Definitions
Discrete Math
Exponents

Geometry
   Euclidean/plane
     conic sections/
       circles
     constructions
     coordinate plane
     triangles/polygons
   higher-dimensional
     polyhedra
   non-Euclidean

Imaginary/Complex
  Numbers
Logic/Set Theory
Number Theory

Physics
Probability
Statistics
Trigonometry

Browse College Modern Algebra

Stars indicate particularly interesting answers or good places to begin browsing.



Two Integers and a Third Degree Polynomial: Square in Z? A Galois Theory Proof [07/28/2010]
A student seeks to prove that there exist infinitely many pairs of non-zero integers such that a particular third degree polynomial is square in the ring of integers. Since the exercise appears in a chapter on Galois theory, Doctor Jacques expands the scope of the question to proving that there are infinitely many such polynomials.

Uniqueness of Ideals [09/23/2003]
How can I prove that in Mn(Q) (the ring of n*n matrices over the rational numbers Q), (0) and Mn(Q) are the only ideals?

Using Galois theory to prove that x^4 +1 is reducible in Z_p[X] for all primes p [11/09/2008]
A student sees a Dr. Math proof that x^4 + 1 is reducible in Z_p[X] for all primes p, but seeks an alternate method -- one using Galois theory.

What is a Torsion Subgroup? [03/05/2003]
Let G be an Abelian group. Show that the elements of finite order in G form a subgroup. This subgroup is called the torsion subgroup of G. Now find the torsion subgroup of the multiplicative group R* of nonzero real numbers.

What is Knot Theory? [03/10/1998]
Researching how knot theory is related to topology and modern algebra.

What Makes Polynomials Relatively Prime? [11/20/2007]
Why are polynomials whose only common factors are constants considered 'relatively prime'? Why are the common constants not considered? For example, 3x + 6 and 3x^2 + 12 are considered relatively prime even though they have a common constant factor of 3.

Zero-Factor Theorem [02/08/2002]
If a and b are real numbers, and if ab = 0, then a = 0 or b = 0. Why the restriction 'a and b are real numbers'?

Page: [<prev]  1  2  3  4  5

Search the Dr. Math Library:

Search: entire archive just College Modern Algebra

Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words


[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help 
_____________________________________

© 1994-2014 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Drexel University School of Education.The Math Forum is a research and educational enterprise of the Drexel University School of Education.