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We give a survey of our recent results on homological properties of Köthe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of Köthe algebras are also presented.

Homological Methods Applied to the Derived Series of Groups

Ralph Strebel (1974)

Commentarii mathematici Helvetici

Honest submodules

Pascual Jara (2007)

Czechoslovak Mathematical Journal

Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular...

Hopfian and co-Hopfian objects.

Kalathoor Varadarajan (1992)

Publicacions Matemàtiques

The aim of the present paper is to study Hopfian and Co-Hopfian objects in categories like the category of rings, the module categories A-mod and mod-A for any ring A. Using Stone's representation theorem any Boolean ring can be regarded as the ring A of clopen subsets of compact Hausdorff totally disconnected space X. It turns out that the Boolean ring A will be Hopfian (resp. co-Hopfian) if and only if the space X is co-Hopfian (resp. Hopfian) in the category Top. For any compact Hausdorff space...

Hyperdéterminant d’un $S L_{2}$ -homomorphisme

Jean Vallès (2008)

Annales mathématiques Blaise Pascal

Etant donnés $A_{1}, \dots, A_{s}$ ( $s \geq 3$ ) des $S L_{2} (ℂ)$ -modules non triviaux de dimensions respectives $n_{1} + 1 \geq \dots \geq n_{s} + 1$ (avec $n_{1} = n_{2} + \dots + n_{s}$ ) et $φ \in ℒ (A_{2} \otimes \dots \otimes A_{s}, A_{1}^{*})$ un $S L_{2} (ℂ)$ -homomorphisme, nous montrons que l’hyperdéterminant de $φ$ est nul sauf si les modules $A_{i}$ sont irréductibles et si l’homomorphisme est la multiplication des polynômes homogènes à deux variables.

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