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Keywords:
hereditary torsion theory; exact; noetherian and perfect torsion theory; Goldie’s torsion theory; precover class; cover class; precover and cover of a module
hereditary torsion theory; exact; noetherian and perfect torsion theory; Goldie’s torsion theory; precover class; cover class; precover and cover of a module
Summary:
In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite type is presented.
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