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Gorenstein projective complexes with respect to cotorsion pairs

Renyu Zhao, Pengju Ma (2019)

Czechoslovak Mathematical Journal

Let ( 𝒜 , ℬ ) be a complete and hereditary cotorsion pair in the category of left R -modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair ( 𝒜 , ℬ ) are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair ( 𝒜 , ℬ ) . As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion pairs possess...

Homology of gaussian groups

Patrick Dehornoy, Yves Lafont (2003)

Annales de l’institut Fourier

We describe new combinatorial methods for constructing explicit free resolutions of ℤ by ℤ G -modules when G is a group of fractions of a monoid where enough lest common multiples exist (“locally Gaussian monoid”), and therefore, for computing the homology of G . Our constructions apply in particular to all Artin-Tits groups of finite Coexter type. Technically, the proofs rely on the properties of least common multiples in a monoid.

On a homology of algebras with unit

Jacek Dębecki (2014)

Annales Polonici Mathematici

We present a very general construction of a chain complex for an arbitrary (even non-associative and non-commutative) algebra with unit and with any topology over a field with a suitable topology. We prove that for the algebra of smooth functions on a smooth manifold with the weak topology the homology vector spaces of this chain complex coincide with the classical singular homology groups of the manifold with real coefficients. We also show that for an associative and commutative algebra with unit...

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