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Eliahou and Kervaire defined splittable monomial ideals and provided a relationship between the Betti numbers of the more complicated ideal in terms of the less complicated pieces. We extend the concept of splittable monomial ideals showing that an ideal which was not splittable according to the original definition is splittable in this more general definition. Further, we provide a generalized version of the result concerning the relationship between the Betti numbers.
Bouchat et al. (Sat,) studied this question.
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