On modules which satisfy the radical formula

Authors: BÜLENT SARAÇ, YÜCEL TIRAŞ

Abstract: In this paper, the authors prove that every representable module over a commutative ring with identity satisfies the radical formula. With this result, they extend the class of modules satisfying the radical formula from that of Artinian modules to a larger one. They conclude their work by giving a description of the radical of a submodule of a representable module.

Keywords: Prime submodule, prime radical, radical formula, secondary module, secondary representation, representable module

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