Finitely Deep Matrices
In the algebraic study of deep matrices DMF on a finite set
of indices over a field, Christopher Kennedy has recently shown that
there is a unique proper ideal Z whose quotient is a central simple
algebra. He showed that this ideal, which doesn't appear for infinite
index sets, is itself a central simple algebra. In this paper we extend
the result to deep matrices with a finite set of 2 or more indices over
an arbitrary coordinate algebra A, showing that when the coordinates are
simple there is again such a unique proper ideal, and in general that
the lattice of ideals of DMA/Z and Z are isomorphic to the lattice of
ideals of the coordinate algebra A.
J. Faulkner < jrf@virginia.edu >
K. McCrimmon < kmm4m@virginia.edu >