Chains of modules with completely reducible quotients

Dauns, John

doi:10.2140/pjm.1966.17.235

Cited by 11 publications

(6 citation statements)

References 5 publications

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“…It is clear that the same preradical is obtained if we close the class X under direct sums and epimorphisms ; thus there is no loss of generality in assuming K closed under direct sums and epimorphisms 4 ). Start with a class 3£ of /?-modules and define F%(M) s the join of all Im η where η ranges over all jR-homomorphisms η : X -> M with all X £ X.…”

Section: Lemma 1 a Preradical F Commutes With Direct Sumsmentioning

confidence: 82%

Torsion preradicals and ascending Loewy series of modules.

1969

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Section: Lemma 1 a Preradical F Commutes With Direct Sumsmentioning

confidence: 82%

Torsion preradicals and ascending Loewy series of modules.

1969

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…(ii). Observe that Theorem 3.1 can be viewed as a generalization of the classical construction of upper and lower Loewy series in representation theory (for definitions, see e.g., [4]). Let V be a finite-dimensional k-vector space.…”

Section: Tits' Centre Conjecture For Fixed Point Subcomplexesmentioning

confidence: 99%

On Tits' Centre Conjecture for fixed point subcomplexes

Bate

Martin

Röhrle

2009

Comptes Rendus. Mathématique

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We give a short and uniform proof of a special case of Tits' Centre Conjecture using a theorem of J.-P. Serre and a result from the authors in 2005. We consider fixed point subcomplexes X H of the building X = X(G) of a connected reductive algebraic group G, where H is a subgroup of G. To cite this article: M. Bate et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). Résumé Sur la conjecture du centre de Tits pour les sous-complexes de points fixes. Nous donnons dans cette Note une démonstration courte et uniforme d'un cas particulier de la conjecture du centre de Tits, en utilisant un théorème de J.-P. Serre et un résultat des auteurs en 2005. Nous considérons les sous-complexes X H de l'immeuble X = X(G) associé à un groupe connexe réductif G, des points fixes de l'action d'un sous-groupe H de G. Pour citer cet article : M. Bate et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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“…If 1 e A, then, of course, the hypothesis (a) of the last corollary holds if and only if A is semisimple with the minimum condition. However, if 1 $ A, there are far more general rings satisfying (a) than merely those with the minimum condition (see [1]). The question arises whether in Theorem III, A -AT-A g JfF with A -M faithful and cyclic implies that A -M is simple.…”

Section: Corollarymentioning

confidence: 99%

“…Remarks 2.7. (1) In particular, if D= D(R -M) and if À: R -> D is the natural map with kernel {r e R | rM=(0)}, then R is dense in D provided A(7?) is dense in the topological sense in X(R) £ D <= MM = n {M\M}, when M has the discrete topology.…”

mentioning

confidence: 99%