Abstract
In this paper, we introduce a new class of monomial ideals, called
d
-fixed ideals, which generalize the class of
p
-Borel ideals and show how some results for
p
-Borel ideals can be transfered to this new class. In particular, we give the form of a principal
d
-fixed ideal and we compute the socle of factors of these ideals. This allowed us to give a generalization of Pardue's formula,i.e. a formula of the regularity for a principal
d
-fixed ideal.