Introduction. Let K be the ring of all n by n matrices over a division ring R. Then each left (right) ideal of K is a principal left (right) ideal generated by an idempotent element. We may, of course, think of K as the ring of all linear transformations of a vector space A (of finite rank) over a division ring R. If we allow the rank of A to be infinite, then it is no longer true that each one sided ideal in the ring of linear transformations is generated by an idempotent element. However, each left (right) ideal which is an annihilator is a principal ideal generated by an idempotent ([1], p. 178). Rings with this property have been termed Baer rings in [12]. Now the vector space A is both a completely reducible module and a free module over R. It is therefore natural to drop the
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