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De l’application des méthodes valuatives en algèbre différentielle

Guillaume Duval (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

La théorie des valuations née des travaux des géomètres et arithméticiens du XIX ê me siècle, fit une apparition tardive et encore peu connue au XX ê me siècle en algèbre différentielle. Dans cet article, à travers les contributions de nombreux auteurs, nous présentons une synthèse des divers apports de la théorie des valuations à l’étude des équations différentielles. Nous insistons sur le caractère unificateur de la théorie des valuations en illustrant comment elles permettent de mettre en parallèle des...

Diversity in inside factorial monoids

Ulrich Krause, Jack Maney, Vadim Ponomarenko (2012)

Czechoslovak Mathematical Journal

In a recent paper (Diversity in Monoids, Czech. Math. J. 62 (2012), 795–809), the last two authors introduced and developed the monoid invariant “diversity” and related properties “homogeneity” and “strong homogeneity”. We investigate these properties within the context of inside factorial monoids, in which the diversity of an element counts the number of its different almost primary components. Inside factorial monoids are characterized via diversity and strong homogeneity. A new invariant complementary...

Diversity in monoids

Jack Maney, Vadim Ponomarenko (2012)

Czechoslovak Mathematical Journal

Let M be a (commutative cancellative) monoid. A nonunit element q ∈ M is called almost primary if for all a , b ∈ M , q ∣ a b implies that there exists k ∈ ℕ such that q ∣ a k or q ∣ b k . We introduce a new monoid invariant, diversity, which generalizes this almost primary property. This invariant is developed and contextualized with other monoid invariants. It naturally leads to two additional properties (homogeneity and strong homogeneity) that measure how far an almost primary element is from being primary. Finally, as an application...

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