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Let $𝒜$ and $ℬ$ be abelian categories with enough projective and injective objects, and $T : 𝒜 \to ℬ$ a left exact additive functor. Then one has a comma category $(ℬ ↓ T)$ . It is shown that if $T : 𝒜 \to ℬ$ is $𝒳$ -exact, then $(^{⊥} 𝒳, 𝒳)$ is a (hereditary) cotorsion pair in $𝒜$ and $(^{⊥} 𝒴, 𝒴)$ ) is a (hereditary) cotorsion pair in $ℬ$ if and only if $((\binom{^{⊥} 𝒳}{^{⊥} 𝒴})), 〈 𝐡 (𝒳, 𝒴) 〉)$ is a (hereditary) cotorsion pair in $(ℬ ↓ T)$ and $𝒳$ and $𝒴$ are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories $𝒜$ and $ℬ$ can induce special preenveloping classes...

Cotorsion-free algebras as endomorphism algebras in $L$ - the discrete and topological cases

Rüdiger E. Göbel, Brendan Goldsmith (1993)

Commentationes Mathematicae Universitatis Carolinae

The discrete algebras $A$ over a commutative ring $R$ which can be realized as the full endomorphism algebra of a torsion-free $R$ -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, $V = L$ . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...

Countably thick modules

Ali Abdel-Mohsen, Mohammad Saleh (2005)

Archivum Mathematicum

The purpose of this paper is to further the study of countably thick modules via weak injectivity. Among others, for some classes $ℳ$ of modules in $σ [M]$ we study when direct sums of modules from $ℳ$ satisfies a property $ℙ$ in $σ [M]$ . In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.

Counting equivalence classes of irreducible representations.

Letzter, Edward S. (2001)

AMA. Algebra Montpellier Announcements [electronic only]

Counting solutions of decomposable form equations

G. R. Everest, K. Győry (1997)

Acta Arithmetica

Counting the number of elements in the mutation classes of $A_{n}$ -quivers.

Bastian, Janine, Prellberg, Thomas, Rubey, Martin, Stump, Christian (2011)

The Electronic Journal of Combinatorics [electronic only]

Covering Spaces in Representation-Theory.

K. Bongartz, P. Gabriel (1981/1982)

Inventiones mathematicae

Coxeter Orbits and Eigenspaces of Frobenius

G. Lusztig (1976)

Inventiones mathematicae

Coxeter polynomials of Salem trees

Charalampos A. Evripidou (2015)

Colloquium Mathematicae

We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities $m ₁, . . ., m_{k}$ for the Coxeter polynomials of the trees $₁, . . .,_{k}$ respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least $m i n m - m ₁, . . ., m - m_{k}$ where $m = m ₁ + \dots + m_{k}$ .

Criteria for shellable multicomplexes.

Popescu, Dorin (2006)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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