Annihilators of principal ideals in the Grassmann algebra
Citation
KOÇ.C., ESİN, S. (2002). Annihilators of principal ideals in the Grassmann algebra. Applications of Geometric Algebra in Computer Science and Engineering. Edited by, L. DORST, C. DORAN, J. LLASENBY. Cambridge, Birkhauser. Volume 3, pp.193-194.Abstract
It is well known that every Frobenius algebra is quasi-Frobenius, that is to say, if a finite dimensional algebra A over a field F has a nondegenerate bilinear form B such that B(xy, z) = B(x, yz) for all x, y, z ∊ A, then the maps L → Ann r (L) and R → Ann l (R) give inclusion preserving bijections between lattices of left and right ideals of A satisfying (a) Ann r (L 1 + L 2) = Ann r (L 1) ⋂ Ann r (L 2), Ann r (L 1 ⋂ L 2) = Ann r (L 1) + Ann r (L 2) (b) Ann l (R 1 + R 2) = Ann l (R 1) ⋂ Ann l (R 2), Ann l (R 1 ⋂ R 2) = Ann l (R 1) + Ann l (R 2) (c) Ann l(Ann r (L)) = LandAnn r (Ann l (R)) = R. (For example see [2].)
