
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 16th, 2018, 06:54 PM  #1 
Member Joined: Sep 2011 Posts: 98 Thanks: 1  Nonzero Polynomials
Hi all, Can someone advise if part (a) is correct? I am not sure how to do part (b). Thanks 
March 16th, 2018, 07:18 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 520 Thanks: 293 Math Focus: Dynamical systems, analytic function theory, numerics 
Part (a) looks fine. For part (b), you should prove that given any field, $F$, the polynomial ring, $F[x]$ is a euclidean domain. From this is easily follows that a polynomial of degree $n$ over any field has at most $n$ roots in that field. Hence, for part (b) the answer is no. 

Tags 
nonzero, polynomials 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Nonzero solutions computation  Gonzalo786  Linear Algebra  4  October 1st, 2016 03:34 PM 
Power Series NonZero Regular Singular Point?  Pfeffernusse  Complex Analysis  1  December 12th, 2009 11:04 PM 
Power Series DE  Nonzero Singular Points?  Pfeffernusse  Calculus  1  December 11th, 2009 01:43 AM 
lagrange polynomials and polynomials...  ElMarsh  Linear Algebra  3  October 15th, 2009 05:14 PM 
nonzero torsion elements  mathsss22  Abstract Algebra  0  November 8th, 2008 11:14 PM 