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Displaying similar documents to “Grothendieck ring of quantum double of finite groups”

FC-modules with an application to cotorsion pairs

Yonghua Guo (2009)

Commentationes Mathematicae Universitatis Carolinae

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Let R be a ring. A left R -module M is called an FC-module if M + = Hom ( M , / ) is a flat right R -module. In this paper, some homological properties of FC-modules are given. Let n be a nonnegative integer and ℱ𝒞 n the class of all left R -modules M such that the flat dimension of M + is less than or equal to n . It is shown that ( ( ℱ𝒞 n ) , ℱ𝒞 n ) is a complete cotorsion pair and if R is a ring such that fd ( ( R R ) + ) n and ℱ𝒞 n is closed under direct sums, then ( ℱ𝒞 n , ℱ𝒞 n ) is a perfect cotorsion pair. In particular, some known results are obtained as...

-cofinitely supplemented modules

H. Çalışıcı, A. Pancar (2004)

Czechoslovak Mathematical Journal

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Let R be a ring and M a right R -module. M is called -cofinitely supplemented if every submodule N of M with M N finitely generated has a supplement that is a direct summand of M . In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R -module is -cofinitely supplemented. In addition, if M has the...

k -torsionless modules with finite Gorenstein dimension

Maryam Salimi, Elham Tavasoli, Siamak Yassemi (2012)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring. It is shown that the finitely generated R -module M with finite Gorenstein dimension is reflexive if and only if M 𝔭 is reflexive for 𝔭 Spec ( R ) with depth ( R 𝔭 ) 1 , and G- dim R 𝔭 ( M 𝔭 ) depth ( R 𝔭 ) - 2 for 𝔭 Spec ( R ) with depth ( R 𝔭 ) 2 . This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for n 2 we give a characterization of n -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally...