Tests for injectivity of modules over commutative rings

• Autores: Lars Winther Christensen, Srikanth B. Iyengar
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 68, Fasc. 2, 2017, págs. 243-250
• Idioma: inglés
• DOI: 10.1007/s13348-016-0176-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • It is proved that a module M over a commutative noetherian ring R is injective if \mathrm {Ext}_{R}^{i}((R/{\mathfrak p})_{\mathfrak p},M)=0 holds for every i\geqslant 1 and every prime ideal \mathfrak {p} in R. This leads to the following characterization of injective modules: If F is faithfully flat, then a module M such that {\text {Hom}}_R(F,M) is injective and {\text {Ext}}^i_R(F,M)=0 for all i\geqslant 1 is injective. A limited version of this characterization is also proved for certain non-noetherian rings.

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