scholarly journals Second Structure Theorem for strong homology☆☆This research was supported by the grant of Russia Fund of Fundamental Researches (Grant # 96-01-01403). The author wishes to thank Professor Sibe Mardešić for editing the manuscript.

2001 ◽  
Vol 113 (1-3) ◽  
pp. 107-134 ◽  
Author(s):  
Ju.T. Lisica
Keyword(s):  
Structure Theorem ◽  
Strong Homology

Existence

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Division Algebra ◽  
Quadratic Forms ◽  
Structure Theorem ◽  
Quadratic Extension ◽  
Quadratic Space ◽  
Division Algebras ◽  
Separable Extension ◽  
Valued Fields ◽  
Quaternion Division Algebra

This chapter proves that Bruhat-Tits buildings exist. It begins with a few definitions and simple observations about quadratic forms, including a 1-fold Pfister form, followed by a discussion of the existence part of the Structure Theorem for complete discretely valued fields due to H. Hasse and F. K. Schmidt. It then considers the generic unramified cases; the generic semi-ramified cases, the generic ramified cases, the wild unramified cases, the wild semi-ramified cases, and the wild ramified cases. These cases range from a unique unramified quadratic space to an unramified separable quadratic extension, a tamely ramified division algebra, a ramified separable quadratic extension, and a unique unramified quaternion division algebra. The chapter also describes ramified quaternion division algebras D₁, D₂, and D₃ over K containing a common subfield E such that E/K is a ramified separable extension.

On Lattice-Ordered Rees Matrix Γ-Semigroups

2013 ◽  
Vol 59 (1) ◽  
pp. 209-218 ◽  
Author(s):  
Kostaq Hila ◽  
Edmond Pisha
Keyword(s):  
Structure Theorem ◽  
Lattice Of Congruences

Abstract The purpose of this paper is to introduce and give some properties of l-Rees matrix Γ-semigroups. Generalizing the results given by Guowei and Ping, concerning the congruences and lattice of congruences on regular Rees matrix Γ-semigroups, the structure theorem of l-congruences lattice of l - Γ-semigroup M = μº(G : I; L; Γe) is given, from which it follows that this l-congruences lattice is distributive.

scholarly journals Quasi-ideal Ehresmann transversals: The spined product structure

2021 ◽  
Vol 19 (1) ◽  
pp. 77-86
Author(s):  
Xiangjun Kong ◽  
Pei Wang ◽  
Jian Tang
Keyword(s):  
Structure Theorem ◽  
Product Structure ◽  
Abundant Semigroup ◽  
Spined Product ◽  
Equivalent Conditions

Abstract In any U-abundant semigroup with an Ehresmann transversal, two significant components R and L are introduced in this paper and described by Green’s ∼ \sim -relations. Some interesting properties associated with R and L are explored and some equivalent conditions for the Ehresmann transversal to be a quasi-ideal are acquired. Finally, a spined product structure theorem is established for a U-abundant semigroup with a quasi-ideal Ehresmann transversal by means of R and L.

scholarly journals Infinite approximate subgroups of soluble Lie groups

2021 ◽  
Author(s):  
Simon Machado
Keyword(s):  
Lie Groups ◽  
Structure Theorem ◽  
Quasi Crystals

AbstractWe study infinite approximate subgroups of soluble Lie groups. We show that approximate subgroups are close, in a sense to be defined, to genuine connected subgroups. Building upon this result we prove a structure theorem for approximate lattices in soluble Lie groups. This extends to soluble Lie groups a theorem about quasi-crystals due to Yves Meyer.

A Structure Theorem for Free Temporal Algebras

1995 ◽  
Vol 41 (2) ◽  
pp. 249-256
Author(s):  
Francisco M. García Olmedo ◽  
Antonio J. Rodríguez Salas
Keyword(s):  
Structure Theorem

A structure theorem forKT-nearfields

1986 ◽  
Vol 31 (1) ◽  
pp. 247-252 ◽  
Author(s):  
William Kerby
Keyword(s):  
Structure Theorem

scholarly journals Towards a classification of rigid product quotient varieties of Kodaira dimension 0

2021 ◽  
Author(s):  
Ingrid Bauer ◽  
Christian Gleissner
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Structure Theorem ◽  
Complete Classification ◽  
Kodaira Dimension ◽  
The Other ◽  
Diagonal Action ◽  
Quotient Varieties ◽  
A Finite Group

AbstractIn this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G. It is shown that only for $$G = {{\,\mathrm{He}\,}}(3), {\mathbb {Z}}_3^2$$ G = He ( 3 ) , Z 3 2 , and only for dimension $$\ge 4$$ ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension 4 is given. For the other finite groups a strong structure theorem for rigid quotients is proven.

scholarly journals Simultaneously vanishing higher derived limits

2021 ◽  
Vol 9 ◽  
Author(s):  
Jeffrey Bergfalk ◽  
Chris Lambie-Hanson
Keyword(s):  
Euclidean Space ◽  
Metric Spaces ◽  
Inverse System ◽  
Finite Support ◽  
Partial Functions ◽  
Weakly Compact ◽  
Compact Cardinal ◽  
Strong Homology ◽  
Finite Support Iteration ◽  
Weakly Compact Cardinal

Abstract In 1988, Sibe Mardešić and Andrei Prasolov isolated an inverse system $\textbf {A}$ with the property that the additivity of strong homology on any class of spaces which includes the closed subsets of Euclidean space would entail that $\lim ^n\textbf {A}$ (the nth derived limit of $\textbf {A}$ ) vanishes for every $n>0$ . Since that time, the question of whether it is consistent with the $\mathsf {ZFC}$ axioms that $\lim ^n \textbf {A}=0$ for every $n>0$ has remained open. It remains possible as well that this condition in fact implies that strong homology is additive on the category of metric spaces. We show that assuming the existence of a weakly compact cardinal, it is indeed consistent with the $\mathsf {ZFC}$ axioms that $\lim ^n \textbf {A}=0$ for all $n>0$ . We show this via a finite-support iteration of Hechler forcings which is of weakly compact length. More precisely, we show that in any forcing extension by this iteration, a condition equivalent to $\lim ^n\textbf {A}=0$ will hold for each $n>0$ . This condition is of interest in its own right; namely, it is the triviality of every coherent n-dimensional family of certain specified sorts of partial functions $\mathbb {N}^2\to \mathbb {Z}$ which are indexed in turn by n-tuples of functions $f:\mathbb {N}\to \mathbb {N}$ . The triviality and coherence in question here generalise the classical and well-studied case of $n=1$ .

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