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The Strong Anick Conjecture is true

Vesselin Drensky, Jie-Tai Yu (2007)

Journal of the European Mathematical Society

Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra $K 〈 x, y, z 〉$ over a field $K$ of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of $K 〈 x, y, z 〉$ . In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a...

The strong persistence property and symbolic strong persistence property

Mehrdad Nasernejad, Kazem Khashyarmanesh, Leslie G. Roberts, Jonathan Toledo (2022)

Czechoslovak Mathematical Journal

Let $I$ be an ideal in a commutative Noetherian ring $R$ . Then the ideal $I$ has the strong persistence property if and only if $(I^{k + 1} :_{R} I) = I^{k}$ for all $k$ , and $I$ has the symbolic strong persistence property if and only if $(I^{(k + 1)} :_{R} I^{(1)}) = I^{(k)}$ for all $k$ , where $I^{(k)}$ denotes the $k$ th symbolic power of $I$ . We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial ideal has the...

Théorème des zéros effectif et élimination

P. Philippon (1989)

Journal de théorie des nombres de Bordeaux

Les paragraphes 1 et 2 rappellent les circonstances de l'exposé oral, tandis que le paragraphe 3 aborde un aspect particulier de la théorie de l'élimination : une notion de multiplicité d'un idéal en un point. Cette partie est le fruit de passionnantes discussions avec F. Amoroso.

Displaying 21 – 35 of 35

The Strong Anick Conjecture is true

The strong persistence property and symbolic strong persistence property

Théorème des zéros effectif et élimination

Théorie de Galois pour une W*-Algèbre

Tight closure and the Kodaira Vanishing Theorem.

Tight closure of an ideal generated by an R-sequence.

Tight closure of parameter ideals.

Topological localization in Fréchet algebras.

Toward an arithmetic of polynomials.

Traces and differential operators over Beilinson completion algebras

Transfer of the notion of $C$ -rings to fibre products. (Transfert de la notion de $C$ -anneaux aux produits fibres.)

Transforms of ideals in a commutative ring.

Twisted forms of finite étale extensions and separable polynomials.

Two-generated ideals of linear type.

Types of Singularity of Components of Difference Polynomials

Currently displaying 21 – 35 of 35