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- W2093853908 abstract "We define and investigate t-semisimple modules as a generalization of semisimple modules. A module M is called t-semisimple if every submodule N contains a direct summand K of M such that K is t-essential in N. T-semisimple modules are Morita invariant and they form a strict subclass of t-extending modules. Many equivalent conditions for a module M to be t-semisimple are found. Accordingly, M is t-semisiple, if and only if, M = Z 2(M) ⊕ S(M) (where Z 2(M) is the Goldie torsion submodule and S(M) is the sum of nonsingular simple submodules). A ring R is called right t-semisimple if R R is t-semisimple. Various characterizations of right t-semisimple rings are given. For some types of rings, conditions equivalent to being t-semisimple are found, and this property is investigated in terms of chain conditions." @default.
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- W2093853908 date "2013-05-20" @default.
- W2093853908 modified "2023-09-24" @default.
- W2093853908 title "T-Semisimple Modules and T-Semisimple Rings" @default.
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- W2093853908 doi "https://doi.org/10.1080/00927872.2011.653065" @default.
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