## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (186.036 recursos)

Publicacions Matemàtique

1. #### Some Local Properties Defining ${\mathcal T}_0$-Groups and Related Classes of Groups

Ballester-Bolinches, A.; Beidleman, J.C.; Esteban-Romero, R.; Ragland, M.F.
We call $G$ a $\operatorname{Hall}_{\mathcal X}$-group if there exists a normal nilpotent subgroup $N$ of $G$ for which $G/N'$ is an ${\mathcal X}$-group. We call $G$ a ${\mathcal T}_0$-group provided $G/\Phi(G)$ is a ${\mathcal T}$-group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define $\operatorname{Hall}_{\mathcal X}$-groups and ${\mathcal T}_0$-groups where ${\mathcal X}\in\{ {\mathcal T},\mathcal {PT},\mathcal {PST}\}$; the classes $\mathcal {PT}$ and $\mathcal {PST}$ denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.

2. #### Extreme Cycles. The Center of a Leavitt Path Algebra

Corrales García, María G.; Martín Barquero, Dolores; Martín González, Cándido; Siles Monlina, Mercedes; Solanilla Hernández, José F.
In this paper we introduce new techniques in order to deepen into the structure of a Leavitt path algebra with the aim of giving a description of the center. Extreme cycles appear for the first time; they concentrate the purely infinite part of a Leavitt path algebra and, jointly with the line points and vertices in cycles without exits, are the key ingredients in order to determine the center of a Leavitt path algebra. Our work will rely on our previous approach to the center of a prime Leavitt path algebra, "Centers of path algebras, Cohn and Leavitt path algebras," Bull. Malays. Math....

3. #### On the Galois Correspondence Theorem in Separable Hopf Galois Theory

Crespo, Teresa; Rio, Anna; Vela, Montserrat
In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that the image of the Galois correspondence does not determine the Hopf Galois structure.

4. #### Upper Bound for Multi-Parameter Iterated Commutators

Dalenc, Laurent; Ou, Yumeng
We show that the product BMO space can be characterized by iterated commutators of a large class of Calderón--Zygmund operators. This result follows from a new proof of boundedness of iterated commutators in terms of the BMO norm of their symbol functions, using Hytönen's representation theorem of Calderón--Zygmund operators as averages of dyadic shifts. The proof introduces some new paraproducts which have BMO estimates.

5. #### Mixed norm estimates for the Riesz transforms on \boldmath$SU(2)$

In this paper we prove mixed norm estimates for Riesz transforms on the group $SU(2)$. From these results vector valued inequalities for sequences of Riesz transforms associated to Jacobi differential operators of different types are deduced.

6. #### Fine Gradings on $\mathfrak e_6$

Draper, Cristina; Viruel, Antonio
There are fourteen fine gradings on the exceptional Lie algebra $\mathfrak e_6$ over an algebraically closed field of zero characteristic. We provide their descriptions and a proof that any fine grading is equivalent to one of them.

7. #### Geometric Characterizations of $p$-Poincaré Inequalities in the Metric Setting

Durand-Cartagena, Estibalitz; Jaramillo, Jesus A.; Shanmugalingam, Nageswari

19. #### Property of rapid decay for extensions of compactly generated groups

Garncarek, Lukasz
n the article we settle down the problem of permanence of property RD under group extensions. We show that if $1\to N\to G\to Q\to 1$ is a short exact sequence of compactly generated groups such that $Q$ has property RD, and $N$ has property RD with respect to the restriction of a word-length on $G$, then $G$ has property RD. ¶ We also generalize the result of Ji and Schweitzer stating that locally compact groups with property RD are unimodular. Namely, we show that any automorphism of a locally compact group with property RD which distorts distances subexponentially, preserves the Haar...

20. #### Minimal Faithful Modules over Artinian Rings

Bergman, George M.
Let $R$ be a left Artinian ring, and $M$ a faithful left $R$-module such that no proper submodule or homomorphic image of $M$ is faithful. ¶ If $R$ is local, and $\operatorname{socle}(R)$ is central in $R$, we show that $\operatorname{length}(M/J(R)M) + \operatorname{length}(\operatorname{socle}(M))\leq \operatorname{length}(\operatorname{socle}(R))+1$. ¶ If $R$ is a finite-dimensional algebra over an algebraically closed field, but not necessarily local or having central socle, we get an inequality similar to the above, with the length of $\operatorname{socle}(R)$ interpreted as its length as a bimodule, and the summand $+1$ replaced by the Euler characteristic of a graph determined by the bimodule structure of $\operatorname{socle}(R)$....

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