Affiliation:
1. Department of Mathematics and Computer Sciences, Physics and Earth Sciences , University of Messina , Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina , Italy
Abstract
Abstract
Let K be a field, E the exterior algebra of a finite dimensional K-vector space, and F a finitely generated graded free E-module with homogeneous basis g
1, . . ., gr
such that deg g
1 ≤ deg g
2 ≤ · · · ≤ deg gr
. We characterize the Hilbert functions of graded E–modules of the type F/M, with M graded submodule of F. The existence of a unique lexicographic submodule of F with the same Hilbert function as M plays a crucial role.
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