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

Abstract.The paper solves completely the existence problem of almostcomplex substructures on spheres.

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