An equivalence between ring F and infinite matrix subring over F (Q909763)

Let F be a ring with identity. Every endomorphism ring A of a free module over F can be considered as a ring of row-finite matrices over F. Let R be a subring of A consisting of matrices with only finitely many non-zero entries. The main result says that Mod-F is equivalent to a complete additive subcategory of Mod-R. Reviewer's remark: More general results on this topic are obtained in the paper [Tsukuba J. Math. 11, 1-16 (1987; Zbl 0627.16031)] of \textit{P. N. Ánh} and \textit{L. Márki}.