Duality for Ideals in the Grassmann Algebra

Abstract

A duality is established between left and right ideals of a finite dimensional Grassmann algebra such that if under the duality a left ideal I and a right ideal J correspond then I is the left annihilator of J and J the right annihilator of I. Another duality is established for two-sided ideals of the Grassmann algebra where two ideals that correspond are annihilators of each other. The dual of the principal ideal generated by an exterior 2-form is completely determined. Q 1996 Academic Press, Inc.