In the present paper, some properties of strongly critical rings are investigated. It is proved that every simple nite ring and each critical ring of order p 2 (p is a prime) are strongly critical. There is an example of critical ring of order 8 which is not strongly critical. It is also proved that if R is a nite ring and Mn(R) is a strongly critical ring, then R is a strongly critical ring. For rings with unity, it is proved that: 1) if R is a nite ring, R/J(R) = Mn(GF(q)) and J(R) is a strongly critical ring, then R is a strongly critical ring; 2) R is strongly critical ring i Mn(R) is a strongly critical ring (for any n ≥ 1).
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