A short proof of Eilenberg and Moore’s theorem
In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
A simple symmetry generating operads related to rooted planar -ary trees and polygonal numbers.
A simplicial description of the homotopy category of simplicial groupoids.
A split exact sequence of Mackey functors.
A Universal Coefficient Theorem for Categories with Kernels.
A Vanishing Theorem in Homological Algebra
About the globular homology of higher dimensional automata
Absolute homology.
Abstract homotopy theory in procategories
Actions and automorphisms of crossed modules
Adjoints, torsion theory and purity.
Affine simplices in Oka manifolds.
Algebra Retracts and Poincaré-Series.
Algebra Structure on Minimal Resolutions of Gorenstein Rings of Embedding Codimension Four.
Algebraic colimit calculations in homotopy theory using fibred and cofibred categories.
Algebraic Vector Bundles over A3 Are Trivial.
Algèbres enveloppantes à homotopie près, homologies et cohomologies
On présente une définition et une construction unifée des homologies et cohomologies d’algèbres et de modules sur ces algèbres et de modules sur ces algèbres dans le cas d’algèbres associatives ou commutatives ou de Lie ou de Gertsenhaber. On sépare la construction linéaire des cogèbres ou bicogèbres qui traduisent les symétries des relations de définition de la structure de la partie structure qui apparaît ici comme une codérivation de degré 1 et de carré nul de la cogèbre ou de la bicogèbre.
Algèbres graphiques (sur un concept de dimension dans les langages formels)
Almost free splitters
Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which are larger...
An addendum and corrigendum to "Almost free splitters" (Colloq. Math. 81 (1999), 193-221)
Let R be a subring of the rational numbers ℚ. We recall from [3] that an R-module G is a splitter if . In this note we correct the statement of Main Theorem 1.5 in [3] and discuss the existence of non-free splitters of cardinality ℵ₁ under the negation of the special continuum hypothesis CH.