Abstract
The purpose of this paper is to completely characterize splitting torsion theories over commutative rings. In particular, if (T, F) is a torsion theory for which T(R) = 0, then (T, F) is a splitting theory if and only if T contains only a finite number of nonisomorphic simple modules and every module in T is semisimple injective. In addition, an ideal theoretic characterization of splitting torsion theories is given, of which one consequence is that splitting torsion theories are TTF; furthermore, if R is also noetherian, then such torsion theories are centrally splitting. The known theorems concerning the splitting of the Goldie and simple torsion theories (for commutative rings) are derived from our theorem.
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