Chapter 5 Polynomial Rings and Factorisation Flashcards
1
Q
What is a root
A
An element a in K is a ROOT of f in K[X] if f(a)=0
2
Q
What is the gcd
A
the greatest common divisor of polynomials f and g is an if d such that d divides f and d divides g, say another polynomial h divides f and g the h will also divide d. d=gcd(f,g)
3
Q
What is a UFD
A
A commutative domain R is said to be a unique factorization domain if every non zero noninvertible elements of R has a unique factorization as a p[roduct or irreducible elements
4
Q
What is a principal ideal domain
A
a principal ideal domain is a commutative domain in which every ideal is principal
5
Q
what is a unit
A
an invertible element
