Extensions of weakly supplemented modules

• Autores: Rafail Alizade, Engin Büyükasik
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 103, Nº 2, 2008, págs. 161-168
• Idioma: inglés
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• Resumen

  • It is shown that weakly supplemented modules need not be closed under extension (i.e. if U and M/U are weakly supplemented then M need not be weakly supplemented). We prove that, if U has a weak supplement in M then M is weakly supplemented. For a commutative ring R, we prove that R is semilocal if and only if every direct product of simple R-modules is weakly supplemented.