Abstract
Throughout this note we consider associative rings with identity and unitary modules. For a module M over a ring R we write MR (resp. aM) to indicate that M is a right (resp. left) R-module. By Soc (MR), Z (MR) and d (MR) we denote the socle, the singular submodule and the Jacobson radical of M R. respectively. A ring R is called semiprimary if the Jacobson radical d of R is nilpotent and the factor ring R/d is semisimple Artinian. A module M is called continuous if (i) every submodule of M is contained essentially in a direct summand of M. and (ii) every submodule of M which is isomorphic to a direct summand of M, is itself a direct summand of M. A ring R is right continuous if R R is continuous. For a detailed study on continuous rings and modules, we refer to [5].
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