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Sia $A$ un anello compatto e sia $M$ un $A$ -modulo localmente compatto. Le dimostrazioni note che $M$ è linearmente topologizzato sembrano alquanto involute ed usano risultati profondi della teoria dei gruppi Abeliani localmente compatti nonché il Teorema di Kaplansky che asserisce che $A$ è linearmente topologizzato. In questa Nota, poggiando sul Teorema di Peter-Weyl, viene esposta una dimostrazione semplice e diretta, della quale il Teorema di Kaplansky è corollario.

Locally complete intersection homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology.

Avramov, Luchezar L. (1999)

Annals of Mathematics. Second Series

Locally finite iterative higher derivations on k[x,y]

Hideo Kojima (2014)

Colloquium Mathematicae

We give a new proof of Miyanishi's theorem on the classification of the additive group scheme actions on the affine plane.

Locally Nilpotent Monomial Derivations

Marek Karaś (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove that every locally nilpotent monomial k-derivation of k[X₁,...,Xₙ] is triangular, whenever k is a ring of characteristic zero. A method of testing monomial k-derivations for local nilpotency is also presented.

Locally Polynomial Algebras are Symmetrie Algebras

H. Bass, E.H. Connell, D.L. Wright (1976)

Inventiones mathematicae

Loewy coincident algebra and $Q F$ -3 associated graded algebra

Hiroyuki Tachikawa (2009)

Czechoslovak Mathematical Journal

We prove that an associated graded algebra $R_{G}$ of a finite dimensional algebra $R$ is $Q F$ (= selfinjective) if and only if $R$ is $Q F$ and Loewy coincident. Here $R$ is said to be Loewy coincident if, for every primitive idempotent $e$ , the upper Loewy series and the lower Loewy series of $R e$ and $e R$ coincide. $Q F$ -3 algebras are an important generalization of $Q F$ algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra $R$ , the associated graded algebra...