Vol. 37, No. 1, 1971

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Torsion theories and rings of quotients of Morita equivalent rings

Darrell R. Turnidge

Vol. 37 (1971), No. 1, 225–234

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.

Mathematical Subject Classification
Primary: 16A08
Received: 4 December 1969
Published: 1 April 1971
Darrell R. Turnidge