Let be an odd prime number and a number field. Let and . Let be the Stickelberger ideal of the group ring defined in the previous paper . As a consequence of a -integer version of a theorem of McCulloh , , it follows that has the Hilbert-Speiser type property for the rings of -integers of elementary abelian extensions over of exponent if and only if the ideal annihilates the -ideal class group of . In this paper, we study some properties of the ideal ,and check whether or not a subfield of satisfies the above property.
"Stickelberger ideals of conductor p and their application." J. Math. Soc. Japan 58 (3) 885 - 902, July, 2006. https://doi.org/10.2969/jmsj/1156342042