Cemal Koç

On generalized Clifford algebras

is a manic irreducible polynomial in R[,

RECURRING-WITH-CARRY SEQUENCES

with a,,+, # 0. If in particular v(e) = 5 1, then the corresponding algebra is called an r-Clifford algebra and denoted by C,(Q, V). In [3], it was shown that any r-Clifford algebra C,(Q, V) is isomorphic, as a vector space, to the special r-Clifford algebra C,(O, V) which may be called an r-exterior algebra. Furthermore, the dimension of r-Clifford algebras over a finite field k with 4 elements was considered, and shown that if dim, V > 2 and Y > & + 1)/2, then C,(Q, V) is of infinite dimension. It was conjectured that C,(Q, V) is infinite dimensional whenever dim, V > 2 and Y > 1 for an arbitrary field k. The purpose of this paper is to give a partial answer to this question.

On a generalization of clifford algebras

In this note we introduce recurring-with-carry sequences which generalize add-withcarry and subtract-with-borrow sequences introduced in [1], and describe periods of admissible recurring-with-carry sequences which include add-with-carry and subtractwith-borrow sequences with a few exceptions.

Annihilators of Principal Ideals in the Grassmann Algebra

Let V be a vector space over a field k, Q a quadratic form on V, T(V) the tensor algebra of IT. We want to study those algebras C generated by 77 having the following property(P)? Any isometry on Vwith respect to Q can be extended to an automorphism of C having invariant V, and conversely, every automorphism of C mapping V onto itself induces an isometry on F’ with respect to Q. The Clifford algebra C(Q, 17) of the quadratic form 0 is a well-known example of such algebras. Clifford algebras may be generalized from various points of views [6, 71, but it would be more natural to make generalizations by means of property (I’). The following proposition furnishes such a generalization.

Stack-sortable permutations and polynomials

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].)