A note on the Matlis dual of a certain injective hull

• Peter Schenzel ^[1]
  1. [1] Martin Luther University Halle-Wittenberg

     Martin Luther University Halle-Wittenberg

     Kreisfreie Stadt Halle, Alemania

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 3 ((March 2015)), 2015 (Ejemplar dedicado a: Special Issue in honor of Prof. Hans-Bjørn Foxby), págs. 666-671
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.05.020
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• Resumen

  • Let (R,m)(R,m) denote a local ring with E=ER(R/m)E=ER(R/m) the injective hull of the residue field. Let p∈SpecR denote a prime ideal with dim⁡R/p=1dim⁡R/p=1, and let ER(R/p)ER(R/p) be the injective hull of R/pR/p. As the main result we prove that the Matlis dual HomR(ER(R/p),E)HomR(ER(R/p),E) is isomorphic to Rpˆ, the completion of RpRp, if and only if R/pR/p is complete. In the case of R a one dimensional domain there is a complete description of Q⊗RRˆ in terms of the completion Rˆ.