A ring of left quotients Q𝒯 of a
ring R can be constructed relative to any hereditary torsion class 𝒯 of left
R-modules. For Morita equivalent rings R and S we construct a one-toone
correspondence between the hereditary torsion classes (strongly complete
Serre classes) of RM and SM and describe the resulting correspondence
between the strongly complete filters of left ideals of R and S. We show
tkat the proper rings of left quotients of R and S relative to corresponding
hereditary torsion classes are Morita equivalent. Applications are made to the
maximal and the classical rings of lefl quotients and the corresponding torsion
theories.
