Resumen de Quasi-Frobenius quotient rings

J. G. Torrecillas, B. T. Jover

• Let R be an associative (not necessarily commutative) ring with unit. The study of flat left R-modules permits to achieve homological characterizations for some kinds of rings (regular Von Neumann, hereditary). Colby investigated in [1] the rings with the property that every left R-module is embedded in a flat left R-module and called them left IF rings. These rings include regular and quasi-Frobenius rings. Another useful tool for the study of non-commutative rings is the classical localization, when it is possible, or the localizations constructed from the most general perspective of torsion theories (mainly the maximal quotient ring). In a recent paper [3] we try to find a relation between these two approximations to the problem of the determination of the structure for general rings. The suggesting idea is that for commutative domains the class of torsionfree modules is exactly the class of submodules of flat modules.

  If Á0 denotes the class of left R-modules that embed in flat left R-modules, we investigate the rings for which this class is the torsionfree class for some hereditary torsion theory t0 on the category of left R-modules, R-Mod.