Several Conclusions About The Maximal Symmetric Quotient Ring And The Martindale Quotient

For a general ring, there is the maximal ring of ringt quotients Qmanr(R), the maximal symmetric ring of quotients Q?(R).For a semiprime ring,there is Martindale ring of ringt quotients Qr(R), Martindale symmetric ring of quo-tients Qs(R). We know that at idempotent element the maximal ring of left quotients of a corner of a ring Qmaxl(eRe) is the corner of the maximal ring of left quotients eQmax1(R)e. In this paper, as for Martindale ring of ringt quo-tients and Martindale symmetric ring of quotients, we obtain similar results adding some conditions. In addition, as for semiprime ring R, the matrix ring of Martindale right quotient ring is the Martindale right quotient ring of maxtri ring. The Martindale symmetric quotient ring have the same result. As for semiprime ring R and S with they are Morita equivalent, we also prove that the ideals generated by two Morita equivalent idempotent rings inside their own Martindale right quotient ring and Martindale symmetric quotient ringis are Morita equivalent.