The Euclidean norm of an element is this is equal to one if and only if . Thus, are the only units.Originally Posted by musicmental85
No, it is not a UFD. Once you have have shown that these elements are irreducible elements the equation shows there is a different factorization.(ii) Show that the elements 3,5, (1+ROOT(-14)) and (1- ROOT(-14))
are irreducible in R
(iii) By considering the equatioion 3.5 = (1+ROOT(-14))(1- ROOT(-14)) show that 3 is not prime in R
(iv) Is R a unique factorisation domain?