On the tameness of trivial extension algebras

Ibrahim Assem; José de la Peña

Displaying similar documents to “On the tameness of trivial extension algebras”

On the category of modules of second kind for Galois coverings

Piotr Dowbor (1996)

Fundamenta Mathematicae

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Let F: R → R/G be a Galois covering and $m o d_{1} (R / G)$ (resp. $m o d_{2} (R / G)$ ) be a full subcategory of the module category mod (R/G), consisting of all R/G-modules of first (resp. second) kind with respect to F. The structure of the categories $(m o d (R / G)) / [m o d_{1} (R / G)]$ and $m o d_{2} (R / G)$ is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.

Periodic sequences of pseudoprimes connected with Carmichael numbers and the least period of the function $l_{x}^{C}$

A. Rotkiewicz (1999)

Acta Arithmetica

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Topological realization of a family of pseudoreflection groups

Dietrich Notbohm (1998)

Fundamenta Mathematicae

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We are interested in a topological realization of a family of pseudoreflection groups $G \subset G L (n, F_{p})$ ; i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants $F_{p} {[x_{1}, . . ., x_{n}]}^{G}$ . Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over $F_{p}$ can appear as the mod-p cohomology of a space. The family under consideration is given by pseudoreflection groups which are subgroups of the wreath product $ℤ / q ≀ Σ_{n}$ where q divides p - 1 and...

Fitting ideals of class groups in a $ℤ_{p}$ -extension

Pietro Cornacchia (1998)

Acta Arithmetica

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The normalizer splitting conjecture for p-compact groups

Kasper Andersen (1999)

Fundamenta Mathematicae

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Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group $W_{X}$ . We prove that for an odd prime p, the fibration $B T \to B N \to B W_{X}$ has a section, which is unique up to vertical homotopy.

Countable partitions of the sets of points and lines

James Schmerl (1999)

Fundamenta Mathematicae

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The following theorem is proved, answering a question raised by Davies in 1963. If $L_{0} \cup L_{1} \cup L_{2} \cup . . .$ is a partition of the set of lines of $ℝ^{n}$ , then there is a partition $ℝ^{n} = S_{0} \cup S_{1} \cup S_{2} \cup . . .$ such that $| ℓ \cap S_{i} | \leq 2$ whenever $ℓ \in L_{i}$ . There are generalizations to some other, higher-dimensional subspaces, improving recent results of Erdős, Jackson Mauldin.

The space of ANR’s in $ℝ^{n}$

Tadeusz Dobrowolski, Leonard Rubin (1994)

Fundamenta Mathematicae

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The hyperspaces $A N R (ℝ^{n})$ and $A R (ℝ^{n})$ in $2^{ℝ^{n}} (n \geq 3)$ consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute $G_{δ σ δ}$ -spaces and that, indeed, they are not $F_{σ δ σ}$ -spaces. The main result is that $A N R (ℝ^{n})$ is an absorber for the class of all absolute $G_{δ σ δ}$ -spaces and is therefore homeomorphic to the standard model space $Ω_{3}$ of this class.

Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension

Alessandro Andretta, Alberto Marcone (1997)

Fundamenta Mathematicae

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We study some natural sets arising in the theory of ordinary differential equations in one variable from the point of view of descriptive set theory and in particular classify them within the Borel hierarchy. We prove that the set of Cauchy problems for ordinary differential equations which have a unique solution is $\prod_{2}^{0}$ -complete and that the set of Cauchy problems which locally have a unique solution is $\sum_{3}^{0}$ -complete. We prove that the set of Cauchy problems which have a global solution is...

The diophantine equation x² + C = yⁿ

J. H. E. Cohn (1993)

Acta Arithmetica

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The minimum uniform compactification of a metric space

R. Grant Woods (1995)

Fundamenta Mathematicae

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It is shown that associated with each metric space (X,d) there is a compactification $u_{d} X$ of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of $u_{d} X$ are presented, and a detailed study of the structure of $u_{d} X$ is undertaken. This culminates in a topological characterization of the outgrowth $u_{d} ℝ^{n} ∖ ℝ^{n}$ , where $(ℝ^{n}, d)$ is Euclidean n-space with its usual metric. ...

Universal spaces in the theory of transfinite dimension, II

Wojciech Olszewski (1994)

Fundamenta Mathematicae

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We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension $ω_{0}$ , or, equivalently, of small transfinite dimension $ω_{0}$ ; that is, the family consists of compact metrizable spaces whose transfinite dimension is $ω_{0}$ , and every compact metrizable space with transfinite dimension $ω_{0}$ is embeddable in a space of the family. We show that the least possible cardinality of such a universal family is equal to the...

The Hasse Principle modulo nth powers

Victor Scharaschkin (1999)

Acta Arithmetica

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Cantor manifolds in the theory of transfinite dimension

Wojciech Olszewski (1994)

Fundamenta Mathematicae

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For every countable non-limit ordinal α we construct an α-dimensional Cantor ind-manifold, i.e., a compact metrizable space $Z_{α}$ such that $i n d Z_{α} = α$ , and no closed subset L of $Z_{α}$ with ind L less than the predecessor of α is a partition in $Z_{α}$ . An α-dimensional Cantor Ind-manifold can be constructed similarly.

Dugundji extenders and retracts on generalized ordered spaces

Gary Gruenhage, Yasunao Hattori, Haruto Ohta (1998)

Fundamenta Mathematicae

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For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an $L_{c h}$ -extender (resp. $L_{c c h}$ -extender) if φ(f)[X] is included in the convex hull (resp. closed convex hull) of f[A] for each f ∈ C(A). Consider the following conditions (i)-(vii) for a closed subset A of a GO-space X: (i) A is a retract of X; (ii) A is a retract of the union of A and all clopen convex components of X; (iii) there is a continuous $L_{c h}$ -extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology...