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In this article, we deal with the problem of monogenity of quintic number fields defined by monic irreducible quadrinomialswith  m  = 2, 3, 4. We give sufficient conditions on  a ,  b ,  c , and  m  so that the index of the field  K  is nontrivial and we evaluatein each case. In particular, if, then  K  is not monogenic. Our results are illustrated by computational examples.

communications in algebra

On index divisors and non-monogenity of certain quintic number fields defined by  x                  5  +  ax                                      m                   +  bx  +  c