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On Distributive Ring and Hereditary Property

For an commutative ring T with identity, we define Distributive ring if any module over T is distributive. In this paper we study and investigate some new relationships between Distributive and hereditary rings. Also, we give many examples and properties of Distributive ring and investigate the behavior of these properties under another ring namely hereditary ring. Also, we also define study these rings and give a characterization of such rings. Some new results have been studied in this paper. Finally, we justify some conditions under which several concepts which are Distributive.