Rudimentary structural matrix rings

초록

The concept of structural matrix rings, studied by van Wyk starting in 1988, is one of the special types of subrings of a full matrix ring over a ring. Before this effort, Edwin Clark used matrix units to define subrings of a full matrix ring over a field. In this paper, we show that the two definitions are equivalent over a ring and we provide further characterizations of structural matrix rings. In addition, we characterize rudimentary structural matrix rings. The cardinals of, respectively, the set of all (non-isomorphic) structural matrix rings, and all (non-isomorphic) rudimentary structural matrix rings, which are subrings of the n×n full matrix ring over Z, are provided.

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