Summand intersection property of modules via z-closed submodules

2021 ◽  
pp. 2250124
Author(s):  
Figen Takil Mutlu ◽  
Adnan Tercan
Keyword(s):  
Direct Summand ◽  
Structural Properties ◽  
Intersection Property ◽  
The Other ◽  
Matrix Rings ◽  
Decomposition Theory ◽  
Morita Invariant ◽  
Closed Submodules

In this paper, we define a module [Formula: see text] to be [Formula: see text] if and only if intersection of each pair of [Formula: see text]-closed direct summands is also a direct summand of [Formula: see text]. We investigate structural properties of [Formula: see text]-modules and locate the implications between the other module properties which are essentially based on direct summands. We deal with decomposition theory as well as direct summands of [Formula: see text]-modules. We apply our results to matrix rings. To this end, it is obtained that the [Formula: see text] property is not Morita invariant.

LANGUAGES WITH A FINITE ANTIDICTIONARY: SOME GROWTH QUESTIONS

2014 ◽  
Vol 25 (08) ◽  
pp. 937-953
Author(s):  
ARSENY M. SHUR
Keyword(s):  
Growth Rate ◽  
Structural Properties ◽  
Exponential Growth ◽  
Regular Languages ◽  
The Other ◽  
Exponential Growth Rate ◽  
Strong Component ◽  
Order Of Growth ◽  
Finite Sets ◽  
Complex Order

We study FAD-languages, which are regular languages defined by finite sets of forbidden factors, together with their “canonical” recognizing automata. We are mainly interested in the possible asymptotic orders of growth for such languages. We analyze certain simplifications of sets of forbidden factors and show that they “almost” preserve the canonical automata. Using this result and structural properties of canonical automata, we describe an algorithm that effectively lists all canonical automata having a sink strong component isomorphic to a given digraph, or reports that no such automata exist. This algorithm can be used, in particular, to prove the existence of a FAD-language over a given alphabet with a given exponential growth rate. On the other hand, we give an example showing that the algorithm cannot prove non-existence of a FAD-language having a given growth rate. Finally, we provide some examples of canonical automata with a nontrivial condensation graph and of FAD-languages with a “complex” order of growth.

scholarly journals Two case studies on structural variation in multilingual settings

2020 ◽  
Vol 5 (1) ◽  
pp. 750
Author(s):  
Ariana Bancu
Keyword(s):  
Case Studies ◽  
Structural Properties ◽  
Language Contact ◽  
Structural Variation ◽  
Mixed Effects ◽  
The Other ◽  
Trajectories Of Change ◽  
Induced Variation ◽  
Shed Light

In this article, I report on two analyses of variation in Transylvanian Saxon (TrSax), an endangered Germanic language in contact with German and Romanian, used in settings predictive of structural influences among languages. My goals are to document the structural properties of the target variables and to evaluate if processes of language contact have an effect on synchronic variation in TrSax. I identified two areas of TrSax that display variation at the morphosyntactic level, and in each case one of the variants has a corresponding structure in German, while the other variant has a corresponding structure in Romanian. To tease apart contact-induced variation from internally motivated variation, I compare data from multilingual speakers with different linguistic profiles and assess the effect of sociolinguistic factors on variation through mixed effects analyses. Variation that patterns similarly across these two groups can provide a clearer account of the structure of TrSax, while differences between the groups can shed light on trajectories of change in TrSax. Furthermore, results of this study have implications for borrowing hierarchies in language contact.

Density functional theory study on the structural, reactivity, and electronic properties of all mono-, di-, tri-, tetra-, and penta-fluoroanilines as monomers for conducting polymers

2012 ◽  
Vol 90 (10) ◽  
pp. 902-914 ◽  
Author(s):  
Hossein Shirani Il Beigi
Keyword(s):  
Density Functional Theory ◽  
Conducting Polymers ◽  
Structural Properties ◽  
Density Functional ◽  
Dipole Moments ◽  
Radical Cations ◽  
The Other ◽  
Functional Theory ◽  
Density Distributions ◽  
Electric Polarizabilities

Electrical and structural properties of mono-, di-, tri-, tetra-, and penta-fluoroanilines as candidate monomers for new conducting polymers have been investigated using hybrid density functional theory (B3LYP/6–311+G**) based methods. The effects of the number and position of the fluorine atoms on the electrical and structural properties of fluoroanilines and their radical cations have also been investigated. The values of the vibrational frequencies, charge and spin-density distributions, ionization potentials, dipole moments, electric polarizabilities, HOMO-LUMO gaps, and the NICS values of these compounds have been calculated and analyzed as well. The results showed that the double bonds in 2-fluoroaniline and 2,5-difluoroaniline are more delocalized compared with other fluoroanilines; therefore, these molecules have the most aptitude for the electropolymerization reactions. The frequency analysis showed that the electrochemical stability of 2-fluoroaniline is greater than the other fluoroanilines. Also, this molecule possesses the largest NICS value compared to the other fluoroanilines. Consequently, 2-fluoroaniline has the largest ring current and the highest conductivity among all other monomers. Based on the results obtained, 2-fluoroaniline and 2,5-difluoroaniline are the best candidate monomers among all fluoroanilines for the synthesis of corresponding conducting polymers.

English in West Africa

2015 ◽  
Author(s):  
Ulrike Gut
Keyword(s):  
West Africa ◽  
Sierra Leone ◽  
Structural Properties ◽  
West African ◽  
The Other ◽  
African Countries ◽  
The West ◽  
Current Role ◽  
British Colonization

This chapter describes the history, role, and structural properties of English in the West African countries the Gambia, Sierra Leone, Liberia, Ghana, Nigeria, the anglophone part of Cameroon, and the island of Saint Helena. It provides an overview of the historical phases of trading contact, British colonization and missionary activities and describes the current role of English in these multilingual countries. Further, it outlines the commonalities and differences in the vocabulary, phonology, morphology, and syntax of the varieties of English spoken in anglophone West Africa. It shows that Liberian Settler English and Saint Helenian English have distinct phonological and morphosyntactic features compared to the other West African Englishes. While some phonological areal features shared by several West African Englishes can be identified, an areal profile does not seem to exist on the level of morphosyntax.

scholarly journals SKEW CATEGORY ALGEBRAS ASSOCIATED WITH PARTIALLY DEFINED DYNAMICAL SYSTEMS

2012 ◽  
Vol 23 (04) ◽  
pp. 1250040 ◽  
Author(s):  
PATRIK LUNDSTRÖM ◽  
JOHAN ÖINERT
Keyword(s):  
Dynamical Systems ◽  
Topological Space ◽  
Large Class ◽  
Additive Group ◽  
Nonzero Ideal ◽  
Intersection Property ◽  
The Other ◽  
The One ◽  
Category Algebras ◽  
The Ideal

We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor s from a category G to Topop and show that it defines what we call a skew category algebra A ⋊σ G. We study the connection between topological freeness of s and, on the one hand, ideal properties of A ⋊σ G and, on the other hand, maximal commutativity of A in A ⋊σ G. In particular, we show that if G is a groupoid and for each e ∈ ob (G) the group of all morphisms e → e is countable and the topological space s(e) is Tychonoff and Baire. Then the following assertions are equivalent: (i) s is topologically free; (ii) A has the ideal intersection property, i.e. if I is a nonzero ideal of A ⋊σ G, then I ∩ A ≠ {0}; (iii) the ring A is a maximal abelian complex subalgebra of A ⋊σ G. Thereby, we generalize a result by Svensson, Silvestrov and de Jeu from the additive group of integers to a large class of groupoids.

scholarly journals Scale-Free Networks with the Same Degree Distribution: Different Structural Properties

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
José H. H. Grisi-Filho ◽  
Raul Ossada ◽  
Fernando Ferreira ◽  
Marcos Amaku
Keyword(s):  
Structural Properties ◽  
Degree Distribution ◽  
Pearson Correlation ◽  
Clustering Coefficient ◽  
The Other ◽  
Scale Free ◽  
Component Size ◽  
Global Efficiency ◽  
Nearest Neighbours ◽  
Scale Free Networks

We have analysed some structural properties of scale-free networks with the same degree distribution. Departing from a degree distribution obtained from the Barabási-Albert (BA) algorithm, networks were generated using four additional different algorithms (Molloy-Reed, Kalisky, and two new models named A and B) besides the BA algorithm itself. For each network, we have calculated the following structural measures: average degree of the nearest neighbours, central point dominance, clustering coefficient, the Pearson correlation coefficient, and global efficiency. We found that different networks with the same degree distribution may have distinct structural properties. In particular, model B generates decentralized networks with a larger number of components, a smaller giant component size, and a low global efficiency when compared to the other algorithms, especially compared to the centralized BA networks that have all vertices in a single component, with a medium to high global efficiency. The other three models generate networks with intermediate characteristics between B and BA models. A consequence of this finding is that the dynamics of different phenomena on these networks may differ considerably.

MODULES WITH COINDEPENDENT MAXIMAL SUBMODULES

2011 ◽  
Vol 10 (01) ◽  
pp. 73-99 ◽  
Author(s):  
PATRICK F. SMITH
Keyword(s):  
Positive Integer ◽  
Direct Summand ◽  
The Other ◽  
Property A ◽  
Other Hand ◽  
Semisimple Module ◽  
Maximal Submodule

Let R be a ring with identity. A unital left R-module M has the min-property provided the simple submodules of M are independent. On the other hand a left R-module M has the complete max-property provided the maximal submodules of M are completely coindependent, in other words every maximal submodule of M does not contain the intersection of the other maximal submodules of M. A semisimple module X has the min-property if and only if X does not contain distinct isomorphic simple submodules and this occurs if and only if X has the complete max-property. A left R-module M has the max-property if [Formula: see text] for every positive integer n and distinct maximal submodules L, Li (1 ≤ i ≤ n) of M. It is proved that a left R-module M has the complete max-property if and only if M has the max-property and every maximal submodule of M/Rad M is a direct summand, where Rad M denotes the radical of M, and in this case every maximal submodule of M is fully invariant. Various characterizations are given for when a module M has the max-property and when M has the complete max-property.

DERIVATIONS ON MORITA RINGS AND GENERALIZED DERIVATIONS

2011 ◽  
Vol 10 (02) ◽  
pp. 191-200 ◽  
Author(s):  
S. AL-NOFAYEE ◽  
S. K. NAUMAN
Keyword(s):  
Homology Theory ◽  
Generalized Derivations ◽  
Matrix Rings ◽  
Morita Invariant ◽  
Generalized Matrix

In this note, derivations on Morita rings (generalized matrix rings) are introduced and generalized derivations on rings are proved to be Morita invariant without involvement of any homology theory.

Sensory Modality and Transmodal Stimulus Properties in Children's Discrimination Learning and Transfer

1976 ◽  
Vol 42 (1) ◽  
pp. 271-278
Author(s):  
Alice G. Vlietstra ◽  
John C. Wright
Keyword(s):  
Structural Properties ◽  
Structural Property ◽  
Sensory Modality ◽  
Transfer Task ◽  
The Other ◽  
Training Task ◽  
Sensory Modalities ◽  
Continuous Tone ◽  
Dim Light ◽  
Significant Interference

72 preschoolers in the 3 conditions were given a 2-choice, 1-dimensional training task in one of 2 sensory modalities, vision or audition, and in one of 2 structural properties: interruptedness or intensity, e.g., flashing (+) vs ongoing (—) light. There followed a 2-dimensional transfer task with 2 new stimulus dimensions varying simultaneously and independently, one in the same sensory modality as the training dimension but with a different structural property, e.g., bright vs dim light; and the other with the same structural property but in a different sensory modality, e.g., pulsed vs continuous tone. The dimension in the same modality was relevant in a modal condition while the dimension with the same structural property was relevant in a transmodal condition. Significant interference resulted when the structural property reinforced in training was incorrect in transfer. No significant facilitation resulted from holding the same modality relevant or keeping the same structural property correct from training to transfer as compared with a control condition where both modality and structural property were changed.

scholarly journals Information structure and referential givenness/newness: How much belongs in the grammar?

2003 ◽  
Author(s):  
Jeanette Gundel
Keyword(s):  
Structural Properties ◽  
Information Structure ◽  
Language Production ◽  
Cognitive Status ◽  
The Other ◽  
Language System ◽  
New Information ◽  
Information Status ◽  
Label Information ◽  
The Way

This paper is concerned with such concepts as topic, focus and cognitive status of discourse referents, which have been included under the label information structure (alternatively information status), as they are related in some sense to the distribution of given and new information. It addresses the question of which information structural properties are best accounted for by grammatical constraints and which can be attributed to non-linguistic constraints on the way information is processed and communicated. Two logically independent senses of given-new information are distinguished, one referential and the other relational. I discuss some examples of linguistic phenomena that pertain to each of these different senses and show that both are linguistically relevant and must be represented in the grammar. I also argue that phenomena related to both senses have pragmatic effects that do not have to be represented in the grammar since they result from interaction of the language system with general pragmatic principles that constrain inferential processes involved in language production and understanding.

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