Author summary (translated from the Chinese): ``A matrix over a division ring is said to be almost zero if all but finitely many of its entries are zero. A matrix ring is said to be almost zero if all its elements are almost zero matrices. In this paper the following main result is obtained: Any simple ring containing minimal one-sided ideals can be imbedded as a module into an almost zero matrix ring over a division ring.'' \par \{The English summary incorrectly says ``cannot'' instead of ``can''.\}