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