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Derivations on prime rings and lie triple systems
No full textBu tezde, asal ve yarı asal halkalar ile 3 lü Lie sistemler üzerinde tanımlı Jordan
türevler üzerine günümüze kadar yapılan çalı¸smalarda elde edilen bazı özelliklere
yer verilmi¸stir.
Bu tez esas olarak be¸s bölümden olu¸smaktadır.
˙Ilk bölümde, tez konusu tanıtılmı¸s ve bu konuyla ilgili yapılmı¸s çalı¸smalar hakkında
kısa bir bilgi verilmi¸stir.
˙Ikinci bölümde, bu tezi anlamada ve okumada kolaylık sa˘glayacak bazı genel
bilgilere ve sonuçlara yer verilmi¸stir.
Üçüncü bölümde, Herstein’ın [13] 1956’daki çalı¸sması esas olarak ele alınmı¸s
ve karakteristi˘gi 2 ve 3’ten farklı olan asal halkaların Jordan homomorfizmaları
incelenmi¸stir.
Dördüncü bölümün ilk iki kısmında herhangi bir halka üzerinde tanımlı her türevin
Jordan türev oldu˘gu ve tersinin ne zaman do˘gru oldu˘guna ili¸skin teoremlere yer
verilmi¸stir. Bu bölümün üçüncü kısmında genelle¸stirilmi¸s Jordan türevin hangi
ko¸sullar altında genelle¸stirilmi¸s türev oldu˘guna ili¸skin çalı¸smaya yer verilmi¸s,
dördüncü kısmında ise benzer çalı¸sma genelle¸stirilmi¸s Jordan 3’lü türevler için
yapılmı¸stır. Yine bu bölümün son iki kısmında, bir asal halka üzerindeki
Jordan (θ ,φ)-türev ile yarı asal halkalar üzerindeki genelle¸stirilmi¸s Jordan 3 lü
(θ ,φ)-türevlerin özelliklerine de˘ginilmi¸stir.
Be¸sinci bölümde, A. Najati’nin 2009 ve 2010 yıllarında yaptı˘gı çalı¸smalar
incelenmi¸stir. Jordan türev ve Jordan 3 lü türev kavramları, 3 lü Lie sistemler
üzerinde tanımlanmı¸s ve bunların dördüncü bölüme paralel olarak bu sistemler
üzerinde sa˘gladıkları özelliklere yer verilmi¸stir.In this thesis, some properties from works which have been done up till now about
Jordan derivations of prime and semiprime rings and Lie triple systems are given.
This thesis essentially consists of five chapters.
In the first chapter, subject of the thesis is introduced and a short information about
the works, done so far related to this subject, is given. In the second chapter, the
general background and results which may help to make the understanding and the
reading of this thesis easier is fixed.
In the third chapter , the work of Herstein [13] which is published in 1956
is considered essentially and the Jordan homomorphisms of prime rings whose
characteristics are different from 2 ve 3 are studied.
In the first and second section of the fourth chapter, some studies which show
that every derivation in rings is a Jordan derivation but each Jordan derivation in
rings is a derivation only under some conditions are studied. In the third section
of the same chapter, the properties of the ring and conditions for that generalized
Jordan derivations in this ring are generalized derivations are given. And in
the fourth section of this chapter, a similar work is obtained for the generalized
Jordan triple derivations. Again in the last two sections of the same chapter, the
properties of the Jordan (θ ,φ)-derivation on a prime ring and generalized Jordan
triple (θ ,φ)-derivations of semiprime rings are mentioned.
In the fifth chapter, A. Najati’s 2009 and 2010 papers are studied. Jordan derivation
and Jordan triple derivation are defined on the Lie triple systems and in the
framework of the fourth chapter, the properties that they satisfy in these systems
are given
Pure özelliği ile tanımlanan modül, halka ve kategori yapıları
Get PDFPURE ÖZELL˙IG˘ ˙I
˙ILE TANIMLANAN
MODÜL, HALKA VE KATEGOR˙I YAPILARI
Azime TARHAN
Doktora Tezi, Matematik Anabilim Dalı
Tez Danı¸smanı: Prof. Dr. Semra DOGRUÖZ ˘
2020, 99 sayfa
Bu tez dört bölümden olu¸smaktadır.
Tezin birinci bölümü olan Giri¸s kısmında tez konusu tanıtılarak konu ile ilgili
temel kabul edilen çalı¸smaların tarihçesi kısaca verilmi¸stir.
˙Ikinci bölümde tezin okunurlugunu kolayla¸stıracak ve ispatlarda kullanılacak ˘
olan bazı temel tanım ve teoremlere yer verilmi¸stir. Ayrıca bu bölümde genel
olarak halka ile modüllere ait bilinen bazı ileri yapısal özellikler ve sonuçlar yer
almaktadır.
Tezin üçüncü bölümünde ilk olarak pure alt modüller ve flat modüllere ait
devamında ise singüler ve nonsingüler modüllere ait bazı temel özellikler
verilmi¸stir. Bu bölümde τs-kapalı alt modüller tanımlanmı¸s ve extending modüller,
bu yeni kapalı alt modüller yardımıyla torsion teoriye göre purely τs-extending
modül olarak genelle¸stirilmi¸stir. Yeni tanımlanan bu extending modüllerin genel
teoride yer alan bazı temel özellikleri sagladı ˘ gı gösterilmi¸stir. Ayrıca flat modüller, ˘
modülün injektif geni¸slemesi ve çarpımsal modüller gibi faktörler kullanılarak
purely τs-extending modüllerin karakterizasyonu yapılmı¸s ve semi-hereditary
halka üzerinde extending modüllerin bir sınıflandırması verilmi¸stir.
Son olarak tezin dördüncü bölümünde pure kapalı alt objeler, güçlü pure kapalı alt
objeler ve sonlu ula¸sılabilir toplamsal kategorilerde pure bölüm Goldie boyut ile
ilgili çalı¸smalar yer almaktadır. Bu kategoride, direkt limitler ve pure epimorfik
görüntüler altında kapalı olan objelerin her sınıfının pure bölüm sonlu boyutlu bir
objesinin her güçlü pure kapalı alt objesinin bir yarı yerel endomorfizma halkasının
var oldugu ispatlanmı¸stır.IÇ˙INDEK˙ILER
KABUL VE ONAY SAYFASI . . . . . . . . . . . . . . . . . . . . . . . . iii
B˙IL˙IMSEL ET˙IK B˙ILD˙IR˙IM SAYFASI . . . . . . . . . . . . . . . . . . . v
ÖZET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
ÖNSÖZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
S˙IMGELER D˙IZ˙IN˙I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
1. G˙IR˙I ¸S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. TEMEL TANIM VE ÖZELL˙IKLER . . . . . . . . . . . . . . . . . . . 10
2.1. Kullanılan Bazı Genel Tanım ve Teoremler . . . . . . . . . . . . . . 10
2.2. Bazı ˙Injektif ve Projektif Modül Özellikleri . . . . . . . . . . . . . . 26
2.3. Bazı Temel Tensör Çarpım Özellikleri . . . . . . . . . . . . . . . . . 29
2.4. Bazı ˙Ileri Modül Özellikleri . . . . . . . . . . . . . . . . . . . . . . 33
3. PURE ALTMODÜLLERE GÖRE EXTENDING MODÜL ÖZELL˙IGˇ ˙I . 41
3.1. Düz (Flat) Modüller ve Pure Altmodüller ile ˙Ilgili Temel Özellikler . . 41
3.2. Singüler Modül ve Bazı Temel Özellikleri . . . . . . . . . . . . . . . 51
3.3. Torsion Teoriye Göre Purely Extending Modüller . . . . . . . . . . . 54
3.4. Torsion Teoriye Göre Purely Extending Modülün Yapılandırılması . . 63
3.5. Torsion Teoriye Göre Purely Extending Modülün Halka ile
Sınıflandırılması . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4. PURE KAPALI ALTOBJELER VE PURE BÖLÜM GOLDIE BOYUT
(PURE QUOTIENT GOLDIE DIMENSION) . . . . . . . . . . . . . . . . 75
4.1. Temel Tanım ve Özellikler . . . . . . . . . . . . . . . . . . . . . . . 76
4.2. Pure Kapalı (Closed) Altobjeler . . . . . . . . . . . . . . . . . . . . 84
4.3. Pure Bölüm Goldie Boyut (Pure Quotient Goldie Dimension) . . . . . 89
KAYNAKLAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
ÖZGEÇM˙I ¸S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
PURE CLOSED SUBOBJECTS AND PURE QUOTIENT GOLDIE DIMENSION
No full textWOS: 000464542900004In this note we introduce pure closed subobjects, strongly pure closed subobjects and pure quotient Goldie dimension in finitely accessible additive categories. Then we give a generalization of a classical dimension formula with respect to their pure closed subobjects. We prove that in this category every strongly pure closed subobject of a pure quotient finite dimensional object of every class of objects closed under direct limits and pure epimorphic images has a semilocal endomorphism ring.Scientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [117F270]; Adnan Menderes University BAPAdnan Menderes University [FEF-17041]The first author is supported by The Scientific and Technological Research Council of Turkey under Grant number 117F270.; Second and third authors are supported by Adnan Menderes University BAP under Grant number FEF-17041
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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