Bicontinuous Isomorphisms between Two Closed Left Ideals of a Compact Dual Ring

1966 ◽  
Vol 18 ◽  
pp. 1148-1151 ◽  
Author(s):  
Ling-Erl E. T. Wu
Keyword(s):  
Natural Generalization ◽  
Minimum Condition ◽  
Topological Ring ◽  
Frobenius Ring ◽  
Frobenius Rings ◽  
The Right ◽  
Left Annihilator ◽  
Number Of Authors ◽  
Dual Ring

A quasi-Frobenius ring is a ring with minimum condition satisfying the conditions r(l)H)) = H and l(r(L)) = L for right ideals H and left ideals L where r(S) (l(S)) denotes the right (left) annihilator of a subset S of the ring. Nakayama first defined and studied such rings (8; 9) and they have been studied by a number of authors (2; 3; 4; 6). A dual ring is a topological ring satisfying the conditions r(l)H)) = H and l(r)H)) = L for closed right ideals H and closed left ideals L. Baer (1) and Kaplansky (7) introduced the notion of such rings, which is a natural generalization of that of quaso-Frobenius rings. Numakura studied the analogy between dual rings and quasi-Frobenius rings in (10).

scholarly journals ON HOMOLOGICAL FROBENIUS COMPLEXES AND BIMODULES

2014 ◽  
Vol 56 (3) ◽  
pp. 629-642
Author(s):  
J. R. GARCÍA ROZAS ◽  
LUIS OYONARTE ◽  
BLAS TORRECILLAS
Keyword(s):  
Associative Ring ◽  
Natural Generalization ◽  
Derived Categories ◽  
Triangulated Categories ◽  
Ring Homomorphisms ◽  
Frobenius Ring ◽  
Gorenstein Categories

AbstractWe introduce the concept of homological Frobenius functors as the natural generalization of Frobenius functors in the setting of triangulated categories, and study their structure in the particular case of the derived categories of those of complexes and modules over a unital associative ring. Tilting complexes (modules) are examples of homological Frobenius complexes (modules). Homological Frobenius functors retain some of the nice properties of Frobenius ones as the ascent theorem for Gorenstein categories. It is shown that homological Frobenius ring homomorphisms are always Frobenius.

Functional Pearl

1996 ◽  
Vol 6 (1) ◽  
pp. 181-188 ◽  
Author(s):  
Graham Hutton ◽  
Erik Meijer
Keyword(s):  
Functional Programming ◽  
Arithmetic Functions ◽  
Special Cases ◽  
Relational Calculus ◽  
The Right ◽  
Number Of Authors

AbstractA representation changer is a function that converts a concrete representation of an abstract value into a different concrete representation of that value. Many useful functions can be recognised as representation changers; examples include compilers and arithmetic functions such as addition and multiplication. Functions that can be specified as the right inverse of other functions are special cases of representation changers. In recent years, a number of authors have used a relational calculus to derive representation changers from their specifications. In this paper, we show that the generality of relations is not essential, and representation changers can be derived within the more basic setting of functional programming. We illustrate our point by deriving a carry-save adder and a base-converter, two functions which have previously been derived relationally.

ON PLOTKIN-OPTIMAL CODES OVER FINITE FROBENIUS RINGS

2006 ◽  
Vol 05 (06) ◽  
pp. 799-815 ◽  
Author(s):  
MARCUS GREFERATH ◽  
GARY McGUIRE ◽  
MICHAEL E. O'SULLIVAN
Keyword(s):  
Hadamard Matrices ◽  
Interesting Property ◽  
Optimal Codes ◽  
Frobenius Ring ◽  
Frobenius Rings ◽  
Plotkin Bound ◽  
Homogeneous Weight ◽  
Finite Frobenius Rings ◽  
Finite Frobenius Ring ◽  
The Relationship

We study the Plotkin bound for codes over a finite Frobenius ring R equipped with the homogeneous weight. We show that for codes meeting the Plotkin bound, the distribution on R induced by projection onto a coordinate has an interesting property. We present several constructions of codes meeting the Plotkin bound and of Plotkin-optimal codes. We also investigate the relationship between Butson–Hadamard matrices and codes over R meeting the Plotkin bound.

scholarly journals On p-injective rings

1995 ◽  
Vol 37 (3) ◽  
pp. 373-378 ◽  
Author(s):  
Gennadi Puninski ◽  
Robert Wisbauer ◽  
Mohamed Yousif
Keyword(s):  
Direct Summand ◽  
Jacobson Radical ◽  
Associative Ring ◽  
The Right ◽  
Left Annihilator

Throughout this paper R will be an associative ring with unity and all R-modules are unitary. The right (resp. left) annihilator in R of a subset X of a module is denoted by r(X)(resp. I(X)). The Jacobson radical of R is denoted by J(R), the singular ideals are denoted by Z(RR) and Z(RR) and the socles by Soc(RR) and Soc(RR). For a module M, E(M) and PE(M) denote the injective and pure-injective envelopes of M, respectively. For a submodule A ⊆ M, the notation A ⊆⊕M will mean that A is a direct summand of M.

scholarly journals A Profile of a Strategic Leader under the Leadership Law in the Czech Armed Forces

2017 ◽  
Vol 22 (3) ◽  
pp. 178-184
Author(s):  
Janka Kosecová ◽  
Petr Cupák
Keyword(s):  
Knowledge Management ◽  
Strategic Management ◽  
Questionnaire Survey ◽  
Armed Forces ◽  
Strategic Thinking ◽  
Point Of View ◽  
John Calvin ◽  
Leadership And Management ◽  
The Right ◽  
Number Of Authors

Abstract From a certain point of view, it can be said that leadership and management are two different things that go hand in hand and complement each other. A number of authors dealing with this issue have long tried to define the exact boundaries between these terms, which, however, may not be entirely beneficial. It is desirable rather to seek appropriate interconnection of both areas in order to ensure the continuous development of the organization. For this reason, the concepts of strategic management, strategic thinking and knowledge management have been clarified. It is possible to apply strategic leadership in the Czech Armed Forces in the right way only by assuming that these areas are used correctly. The aim of the article is to present the current leader profile at a strategic level under the Leadership laws, using the theory developed by major author John Calvin Maxwell. The article details the results of the questionnaire survey. The strong, average and weak areas of leadership capabilities of the organization's top management are clearly identified. In conclusion, the most important recommendations are proposed to improve the current situation.

scholarly journals Enumeration of Cylindric Plane Partitions

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Robin Langer
Keyword(s):  
Natural Generalization ◽  
Path Model ◽  
Plane Partition ◽  
Combinatorial Interpretation ◽  
Plane Partitions ◽  
Generating Series ◽  
International Audience ◽  
The Individual ◽  
The Right ◽  
Reverse Plane

International audience Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. As in the reverse plane partition case, the right hand side of this identity admits a simple factorization form in terms of the "hook lengths'' of the individual boxes in the underlying shape. The first result of this paper is a new bijective proof of Borodin's identity which makes use of Fomin's growth diagram framework for generalized RSK correspondences. The second result of this paper is a $(q,t)$-analog of Borodin's identity which extends previous work by Okada in the reverse plane partition case. The third result of this paper is an explicit combinatorial interpretation of the Macdonald weight occurring in the $(q,t)$-analog in terms of the non-intersecting lattice path model for cylindric plane partitions. Les partitions planes cylindriques sont une généralisation naturelle des partitions planes renversées. Une série génératrice pour énumération des partitions planes cylindriques a été donnée récemment par Borodin. Comme dans le cas des partitions planes renversées, la partie droite de cette identité peut être factoriser en terme de "longueur d’équerres'' des carrés dans la forme sous-jacente. Le premier résultat de cet article est une nouvelle preuve bijective de l'identité de Borodin qui utilise le cadre de "diagramme de croissance'' de Fomin pour la correspondance de RSK généralisée. Le deuxième résultat de cette article est une $(q,t)$-déformation d'identité de Borodin qui généralise un résultat de Okada dans le cas des partitions planes renversées. Le troisième résultat de cet article est une formule combinatoire explicite pour le poids de Macdonald qui utilise le modèle des chemins non-intersectant pour les partitions planes cylindriques.

scholarly journals Title Length Variation Trends in Papers on Algorithms in IEEE Xplore

2021 ◽  
Author(s):  
Mohammad Reza Besharati ◽  
Nafiseh Jafari ◽  
Mohammad Izadi
Keyword(s):  
Statistical Analysis ◽  
Extensive Study ◽  
Scientific Discipline ◽  
Length Variation ◽  
The Right ◽  
Variation Trends ◽  
Over Time ◽  
Number Of Authors

Abstract The title of any paper showcases its identity and the scientific orientation of its authors. The title length is one of the scientometrics indicators used in the statistical analysis of papers. The researchers have already found a relationship between the number of authors of a paper and its title length. In this study, we have analyzed the metadata of 19,469 papers on algorithms indexed in the IEEE Xplore database to conduct a more extensive study on this indicator and its trends, with three major findings: 1) Over time, the title lengths of the algorithm-related papers have increased, going from 70 printed letters in 1995 to 80 in 2009; 2) Papers with more authors also have longer titles; and 3) With time, as more scholars delve into the subfields of a scientific discipline, the title lengths of papers would increase. So that the peaks of the frequency charts of this variable exhibit a wave-like behavior and shift to the right.

scholarly journals A ONE-SIDED PRIME IDEAL PRINCIPLE FOR NONCOMMUTATIVE RINGS

2010 ◽  
Vol 09 (06) ◽  
pp. 877-919 ◽  
Author(s):  
MANUEL L. REYES
Keyword(s):  
Prime Ideal ◽  
Minimum Condition ◽  
Noncommutative Rings ◽  
Special Subset ◽  
Similarities And Differences ◽  
The One ◽  
The Right ◽  
Specific Sense ◽  
Completely Prime Ideal ◽  
General Ring

Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these right ideals and their commutative counterparts. We prove the Completely Prime Ideal Principle, a theorem stating that right ideals that are maximal in a specific sense must be completely prime. We offer a number of applications of the Completely Prime Ideal Principle arising from many diverse concepts in rings and modules. These applications show how completely prime right ideals control the one-sided structure of a ring, and they recover earlier theorems stating that certain noncommutative rings are domains (namely, proper right PCI rings and rings with the right restricted minimum condition that are not right artinian). In order to provide a deeper understanding of the set of completely prime right ideals in a general ring, we study the special subset of comonoform right ideals.

Classification of five-dimensional naturally reductive spaces

1985 ◽  
Vol 97 (3) ◽  
pp. 445-463 ◽  
Author(s):  
Oldřich Kowalski ◽  
Lieven Vanhecke
Keyword(s):  
General Theory ◽  
Symmetric Spaces ◽  
Homogeneous Spaces ◽  
Natural Generalization ◽  
Riemannian Symmetric Spaces ◽  
Reductive Homogeneous Spaces ◽  
Naturally Reductive ◽  
Volume Preserving ◽  
Number Of Authors

Naturally reductive homogeneous spaces have been studied by a number of authors as a natural generalization of Riemannian symmetric spaces. A general theory with many examples was well-developed by D'Atri and Ziller[3]. D'Atri and Nickerson have proved that all naturally reductive spaces are spaces with volume-preserving local geodesic symmetries (see [1] and [2]).

Victims of natural disaster and the right to humanitarian assistance: A practitioner's view

1998 ◽  
Vol 38 (325) ◽  
pp. 611-617
Author(s):  
Peter Walker
Keyword(s):  
Natural Disaster ◽  
Humanitarian Assistance ◽  
The Right ◽  
Number Of Authors ◽  
Legal Right

A number of authors, notably Hardcastle and Chua writing in this issue of the Review, have recently argued the case for either the existence of an international legal right to humanitarian assistance or the need to speedily establish such a right.

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