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- W2004292476 abstract "A module M is called a CS-module if every submodule of M is essential in a direct summand of M. A ring R is called CS-semisimple if every right R-module is CS. For a ring R, we show that: is right artinian with Jacobson radical cube zero if every countably generated right -module is a direct sum of a projective module and a CS-module. The following conditions are equivalent: (i) Every countably generated right -module is a direct sum of a projective module and a quasicontinuous module; and (ii) every right -module is a direct sum of a projective module and a quasi-injective module. We describe the structure of rings in (2) and show that such a ring is not necessarily CS-semisimple." @default.
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- W2004292476 date "2000-01-01" @default.
- W2004292476 modified "2023-09-28" @default.
- W2004292476 title "On Some Classes of Artinian Rings" @default.
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- W2004292476 doi "https://doi.org/10.1006/jabr.1999.8080" @default.
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