Xin Lin
Abstract
The main aim is to give some necessary and sufficient conditions that the τ-Jacobson radical of a module is τ-Artinian and to show that the module M is τ-Artinian if and only if M satisfies DCC on superflous submodules and J τ(M) is τ-semicritical.
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The main aim is to give some necessary and sufficient conditions that the τ-Jacobson radical of a module is τ-Artinian and to show that the module M is τ-Artinian if and only if M satisfies DCC on superflous submodules and J τ(M) is τ-semicritical.
Key concepts: Jacobson radical, Semisimple module, Mathematics, Artinian ring, Pure mathematics, Algebra over a field, Noncommutative ring, Ring (chemistry)