Masatoshi Ikeda

On generalized Clifford algebras

is a manic irreducible polynomial in R[,

On the dimension of modules and algebras. I

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.