Maximal orders in a finite-dimensional central simple algebra over a valuation ring of height 1

This paper consists of two sections. In §  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 $V$-orders in the matrix ring $K_n$, where $V$ is a valuation ring of height 1 in the field $K$. 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.
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