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FC-modules with an application to cotorsion pairs

Yonghua Guo (2009)

Commentationes Mathematicae Universitatis Carolinae

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 corollaries....

Finiteness aspects of Gorenstein homological dimensions

Samir Bouchiba (2013)

Colloquium Mathematicae

We present an alternative way of measuring the Gorenstein projective (resp., injective) dimension of modules via a new type of complete projective (resp., injective) resolutions. As an application, we easily recover well known theorems such as the Auslander-Bridger formula. Our approach allows us to relate the Gorenstein global dimension of a ring R to the cohomological invariants silp(R) and spli(R) introduced by Gedrich and Gruenberg by proving that leftG-gldim(R) = maxleftsilp(R), leftspli(R),...

Finiteness of the strong global dimension of radical square zero algebras

Otto Kerner, Andrzej Skowroński, Kunio Yamagata, Dan Zacharia (2004)

Open Mathematics

The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density...

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