Abstract
This paper consists of two sections. In § 1 maximal, almost maximal, and
complete valuation rings are characterized in terms of the decomposability of torsion-free modules of rank 2. In § 2 an attempt is made to describe the maximal
-orders in the matrix ring 
, where is a valuation ring of height 1
in the field 
. Also, § 2 contains a generalization to a matrix algebra
over a field of the well-known fact that a maximal subring of a field is either
a field or a valuation ring of
height 1.
Bibliography: 9 titles.