Arithmetic of Matrices Over Dedekind Domains

Abstract

In previous papers [7], [9], we had dealt with some aspects of the theory of arithmetical functions defined on the set of matrices with entries from the ring Z of (rational) integers.
The fact that reasonable arithmetic may be done over a Dedekind domain o, makes it natural to expect an extension to the situation where Z is replaced by o. This has been noted already in the recent work of Bhandari [1], Sunder Lal [6], Narang [10], [11], [12] and the author [7] and [9].