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Citation - WoS: 14
Citation - Scopus: 11
Extensions of Weakly Supplemented Modules
(Mathematica Scandinavica, 2008) Alizade, Rafail; Büyükaşık, Engin
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.
Citation - WoS: 10
Citation - Scopus: 10
Special Precovers in Cotorsion Theories
(Cambridge University Press, 2002) Akıncı, Karen D.; Alizade, Rafail
A cotorsion theory is defined as a pair of classes Ext-orthogonal to each other. We give a hereditary condition (HC) which is satisfied by the (flat, cotorsion) cotorsion theory and give properties satisfied by arbitrary cotorsion theories with an HC. Given a cotorsion theory with an HC, we consider the class of all modules having a special precover with respect to the first class in the cotorsion theory and show that this class is closed under extensions. We then raise the question of whether this class is resolving or coresolving.

Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection