A Module whose prime Spectrum has the Surjective Natural Map

• Autores: Chin-Pi Lu
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 1, 2007, págs. 125-143
• Idioma: inglés
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• Resumen

  • Let R be a commutative ring with identity. The purpose of this paper is to introduce a new class of modules over R called primeful R-modules. Every nonzero primeful module possesses the non-empty prime spectrum with the surjective natural map. This class contains the family of finitely generated R-modules properly. We show that the theory of prime submodules of primeful modules resembles to that of finitely generated modules.