Categorification of the virtual braid groups
We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.
Cellular covers of cotorsion-free modules
In this paper we improve recent results dealing with cellular covers of R-modules. Cellular covers (sometimes called colocalizations) come up in the context of homotopical localization of topological spaces. They are related to idempotent cotriples, idempotent comonads or coreflectors in category theory. Recall that a homomorphism of R-modules π: G → H is called a cellular cover over H if π induces an isomorphism , where π⁎(φ) = πφ for each (where maps are acting on the left). On the one hand,...
Centres and Fixed-Point Rings of Artinian Rings.
Certain Complexes Associated to a Sequence and a Matrix.
CF-modules over commutative rings
Let be a commutative ring with unit. We give some criterions for determining when a direct sum of two CF-modules over is a CF-module. When is local, we characterize the CF-modules over whose tensor product is a CF-module.
Chains of factorizations in orders of global fields
Chains of factorizations in weakly Krull domains
Chains of free modules and construction of -free modules
Challenging problems on affine -space
Champs de vecteurs et formes différentielles sur une variété des points proches
Let be a smooth manifold, a local algebra in sense of André Weil, the manifold of near points on of kind and the module of vector fields on . We give a new definition of vector fields on and we show that is a Lie algebra over . We study the cohomology of -differential forms. Résumé. On considère une variété différentielle, une algèbre locale au sens d’André Weil, la variété des points proches de d’espèce et le module des champs de vecteurs sur . On donne une nouvelle...
Characteristic of Rings. Prime Fields
The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.
Characterization of Fans and Hereditarily Pythagorean Fields.
Characterization of rational and algebraic power series
Characterization of the Hilbert-Samuel polynomials of curve singularities
Characterizations of Buchsbaum Complexes.
Characterizations of Lambek-Carlitz type
We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full binomial type. The -analog of the Lambek-Carlitz type characterization of exponential series is also established.
Characterizations of some rings with -projective, -(FP)-injective and -flat modules
Let be a commutative ring and a semidualizing -module. We investigate the relations between -flat modules and -FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.
Charakerisierung der lokalbeschränkten Ringtopologien auf globalen Körpern.
Charakterisierungen der primitiven Klassen arithmetischer Ringe.
Charles Hermite’s stroll through the Galois fields
Although everything seems to oppose the two mathematicians, Charles Hermite’s role was crucial in the study and diffusion of Évariste Galois’s results in France during the second half of the nineteenth century. The present article examines that part of Hermite’s work explicitly linked to Galois, the reduction of modular equations in particular. It shows how Hermite’s mathematical convictions—concerning effectiveness or the unity of algebra, analysis and arithmetic—shaped his interpretation of Galois...