scholarly journals A lattice-theoretic characterization of pure subgroups of Abelian groups

2021 ◽  
Author(s):  
M. Ferrara ◽  
M. Trombetti
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Subgroup Lattice ◽  
General Definition ◽  
Short Paper ◽  
Theoretic Characterization ◽  
Definition Of

AbstractLet G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

Spectral synthesis and residually finite-dimensional algebras

2017 ◽  
Vol 16 (10) ◽  
pp. 1750200 ◽  
Author(s):  
László Székelyhidi ◽  
Bettina Wilkens
Keyword(s):  
Spectral Analysis ◽  
Abelian Group ◽  
Theoretical Approach ◽  
Abelian Groups ◽  
Spectral Synthesis ◽  
Residually Finite ◽  
Finite Dimensional ◽  
Analysis And Synthesis ◽  
Spectral Analysis And Synthesis

In 2004, a counterexample was given for a 1965 result of R. J. Elliott claiming that discrete spectral synthesis holds on every Abelian group. Since then the investigation of discrete spectral analysis and synthesis has gained traction. Characterizations of the Abelian groups that possess spectral analysis and spectral synthesis, respectively, were published in 2005. A characterization of the varieties on discrete Abelian groups enjoying spectral synthesis is still missing. We present a ring theoretical approach to the issue. In particular, we provide a generalization of the Principal Ideal Theorem on discrete Abelian groups.

scholarly journals A Generalization of Final Rank of Primary Abelian Groups

1970 ◽  
Vol 22 (6) ◽  
pp. 1118-1122 ◽  
Author(s):  
Doyle O. Cutler ◽  
Paul F. Dubois
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Basic Subgroup ◽  
Primary Abelian Group ◽  
Limit Ordinal ◽  
Final Rank ◽  
Definition Of ◽  
Group Recall

Let G be a p-primary Abelian group. Recall that the final rank of G is infn∈ω{r(pnG)}, where r(pnG) is the rank of pnG and ω is the first limit ordinal. Alternately, if Γ is the set of all basic subgroups of G, we may define the final rank of G by supB∈Γ {r(G/B)}. In fact, it is known that there exists a basic subgroup B of G such that r(G/B) is equal to the final rank of G. Since the final rank of G is equal to the final rank of a high subgroup of G plus the rank of pωG, one could obtain the same information if the definition of final rank were restricted to the class of p-primary Abelian groups of length ω.

scholarly journals Le lingála dans l’enseignement des sciences dans les écoles de Kinshasa. Une approche socioterminologique

Afrika Focus ◽  
2013 ◽  
Vol 26 (2) ◽  
pp. 142-150
Author(s):  
Bienvenu Sene Mongaba
Keyword(s):  
General Definition ◽  
Scientific Concept ◽  
African Countries ◽  
African Languages ◽  
Bantu Languages ◽  
Science Courses ◽  
Verb Phrases ◽  
Teachers And Students ◽  
Definition Of

In most African countries, former colonial languages are still used as languages of instruction in the school system, especially for science courses in secondary schools and in universities, although, ironically, proficiency in former colonial languages is dwindling. At the same time, however, African languages lack in specialized terminology to accommodate teaching. Empowering African languages is therefore becoming urgent, so that teachers can use them efficiently as languages of instruction. My PhD work strives to provide a solution to that problem by finding tools for the empowerment of the vocabulary and scientific discourse of Lingála, as well as its validation and diffusion among teachers and students of Kinshasa. This is why my PhD work aims at analyzing morpho-semantics of derivatives (verbs, deverbal nouns, nominals), since in Bantu languages, as widely established, derivation and compounding are very productive. I have systematically extracted general meanings from each combination of affixes (nominal prefix-verbal extension-final vowel). While doing so, I have created a derivative generator, i.e. a table where, by replacing a certain verbal stem, a list of nouns and verbs candidates is generated, alongside a brief definition allowing a terminologist to link a certain term to a certain scientific concept the specific definition of which best fits the general definition. The ultimate goal is the coinage of scientific terms. Creating specialty terms is useful, but fining those terms in a discourse also needs characterization of the language syntax requirements and limits. Therefore, I have then moved on to analyzing and describing noun phrases and verb phrases structures. Following that, I have then worked on verifying if the terms coined really fit in natural Lingála language, through tests designed to identify and distinguish verb and sentence complements. Having theorized the morpho-semantics and the syntax of Lingála, I have applied it in writing chemistry text in Lingála. I have conducted all of my PhD work in Lingála, which means I have conceived and written my PhD work in Lingála. Doing so has also allowed me to coin linguistics terms and discourse in Lingála.

scholarly journals Pointed finite tensor categories over abelian groups

2017 ◽  
Vol 28 (11) ◽  
pp. 1750087
Author(s):  
Iván Angiono ◽  
César Galindo
Keyword(s):  
Abelian Group ◽  
Cohomology Class ◽  
Hopf Algebras ◽  
Abelian Groups ◽  
Tensor Category ◽  
Tensor Categories ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras

We give a characterization of finite pointed tensor categories obtained as de-equivariantizations of the category of corepresentations of finite-dimensional pointed Hopf algebras with abelian group of group-like elements only in terms of the (cohomology class of the) associator of the pointed part. As an application we prove that every coradically graded pointed finite braided tensor category is a de-equivariantization of the category of corepresentations of a finite-dimensional pointed Hopf algebras with abelian group of group-like elements.

Hypercyclic Abelian Groups of Affine Maps on ℂn

2013 ◽  
Vol 56 (3) ◽  
pp. 477-490 ◽  
Author(s):  
Adlene Ayadi
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Dense Orbit ◽  
Finitely Generated ◽  
Affine Maps

Abstract.We give a characterization of hypercyclic abelian group 𝒢 of affine maps on ℂn. If G is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by n affine maps on Cn has a dense orbit.

scholarly journals Rainbow-free $3$-colorings of Abelian Groups

10.37236/2054 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Amanda Montejano ◽  
Oriol Serra
Keyword(s):  
Abelian Group ◽  
Arithmetic Progression ◽  
Structural Characterization ◽  
Abelian Groups ◽  
Cyclic Groups ◽  
Chromatic Class

A $3$-coloring of the elements of an abelian group is said to be rainbow-free if there is no $3$-term arithmetic progression with its members having pairwise distinct colors. We give a structural characterization of rainbow-free colorings of abelian groups. This characterization proves a conjecture of Jungić et al. on the size of the smallest chromatic class of a rainbow-free $3$-coloring of cyclic groups.

The distribution of sequences in Abelian groups

1970 ◽  
Vol 67 (1) ◽  
pp. 1-11 ◽  
Author(s):  
J. S. Dennis
Keyword(s):  
Abelian Group ◽  
Uniform Distribution ◽  
Abelian Groups ◽  
Definition Of ◽  
Independent Distribution ◽  
Prime Exponent

1Introduction. In this paper, I give a definition of uniform distribution for sequences taking values in certain types of Abelian group—in particular, in groups of prime exponent—and one of independent distribution for sets of such sequences. In the various cases, I find conditions for the properties to hold, which are similar to Weyl's criterion for the uniform distribution of real sequences modulo 1.

A Homological characterization of certain Abelian groups

1961 ◽  
Vol 57 (2) ◽  
pp. 256-264 ◽  
Author(s):  
A. J. Douglas
Keyword(s):  
Abelian Group ◽  
Homology Group ◽  
Abelian Groups ◽  
Unit Element ◽  
Homology Theory ◽  
Homology Groups ◽  
Complete Answer ◽  
Homological Characterization

Let G be a monoid; that is to say, G is a set such that with each pair σ, τ of elements of G there is associated a further element of G called the ‘product’ of σ and τ and written as στ. In addition it is required that multiplication be associative and that G shall have a unit element. The so-called ‘Homology Theory’† associates with each left G-module A and each integer n (n ≥ 0) an additive Abelian group Hn (G, A), called the nth homology group of G with coefficients in A. It is natural to ask what can be said about G if all the homology groups of G after the pth vanish identically in A. In this paper we give a complete answer to this question in the case when G is an Abelian group. Before describing the main result, however, it will be convenient to define what we shall call the homology type of G. We write Hn(G, A) ≡ 0 if Hn(G, A) = 0 for all left G-modules A.

scholarly journals On elementary loops of logic programs

2011 ◽  
Vol 11 (6) ◽  
pp. 953-988 ◽  
Author(s):  
MARTIN GEBSER ◽  
JOOHYUNG LEE ◽  
YULIYA LIERLER
Keyword(s):  
Nonmonotonic Reasoning ◽  
The Body ◽  
The Other ◽  
Stable Model ◽  
Logic Programs ◽  
Graph Theoretic ◽  
Theoretic Characterization ◽  
Definition Of ◽  
Disjunctive Programs

AbstractUsing the notion of an elementary loop, Gebser and Schaub (2005. Proceedings of the Eighth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05), 53–65) refined the theorem on loop formulas attributable to Lin and Zhao (2004) by considering loop formulas of elementary loops only. In this paper, we reformulate the definition of an elementary loop, extend it to disjunctive programs, and study several properties of elementary loops, including how maximal elementary loops are related to minimal unfounded sets. The results provide useful insights into the stable model semantics in terms of elementary loops. For a nondisjunctive program, using a graph-theoretic characterization of an elementary loop, we show that the problem of recognizing an elementary loop is tractable. On the other hand, we also show that the corresponding problem is coNP-complete for a disjunctive program. Based on the notion of an elementary loop, we present the class of Head-Elementary-loop-Free (HEF) programs, which strictly generalizes the class of Head-Cycle-Free (HCF) programs attributable to Ben-Eliyahu and Dechter (1994. Annals of Mathematics and Artificial Intelligence 12, 53–87). Like an HCF program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body.

scholarly journals A VALUATION THEORETIC CHARACTERIZATION OF RECURSIVELY SATURATED REAL CLOSED FIELDS

2015 ◽  
Vol 80 (1) ◽  
pp. 194-206 ◽  
Author(s):  
PAOLA D’AQUINO ◽  
SALMA KUHLMANN ◽  
KAREN LANGE
Keyword(s):  
Abelian Group ◽  
Real Closed Field ◽  
Closed Field ◽  
Real Closed Fields ◽  
Closed Fields ◽  
Theoretic Characterization ◽  
Image Position ◽  
Recursively Saturated

AbstractWe give a valuation theoretic characterization for a real closed field to be recursively saturated. This builds on work in [9], where the authors gave such a characterization for κ-saturation, for a cardinal $\kappa \ge \aleph _0 $. Our result extends the characterization of Harnik and Ressayre [7] for a divisible ordered abelian group to be recursively saturated.

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