All hereditary torsion theories are differential

• Autores: Christian Lomp , John Van den Berg
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 213, Nº 4, 2009, págs. 476-478
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2008.07.018
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let a and ß be automorphisms on a ring R and d:R?R an (a,ß)-derivation. It is shown that if is a right Gabriel filter on R then is d-invariant if it is both a and ß-invariant. A consequence of this result is that every hereditary torsion theory on the category of right R-modules is differential in the sense of Bland (2006). This answers in the affirmative a question posed by Va� (2007) and strengthens a result due to Golan (1981) on the extendability of a derivation map from a module to its module of quotients at a hereditary torsion theory.