21 research outputs found
DEĞİŞMELİ OLMAYAN HALKALARDA COHEN VE KAPLANSKY TEOREMLERİNİN GENELLEMELERİ
No full textIn commutative setting, prime ideals are very important tools to determine the structure
of a ring. In this thesis, some structure theorems will be discussed which belong to
Cohen and Kaplansky. The aim of this thesis is to examine the noncommutative generalizations
of Cohen and Kaplansky Theorems, especially considering Reyes’s works in
2010 and 2012. The introductory chapter consists of informations about the importance
and the historical improvement of the thesis subject. The second chapter contains basic
information needed throughout the thesis. In the third chapter, Cohen and Kaplansky
Theorems and their roles in commutative rings are emphasized. Also, S-Noetherian
ring structure which was defined by Anderson and Dumitrescu is introduced and some
features of this structure are indicated. In the fourth chapter, one-sided generalizations
of prime ideals in noncommutative settings are examined and some concepts like
completely prime ideals and Oka families are described. Their role in the structure of
a noncommutative ring is examined with applications. The fifth chapter is concerned
with the noncommutative generalizations of Cohen and Kaplansky Theorems by the
Oka families and the point annihilator sets. In the last chapter, noncommutative generalizations
of Cohen and Kaplansky Theorems obtained by different approaches are
investigated. Among the generalizations discussed by Koh, Chandran and Michler, the
noncommutative generalization of S-Noether ring structure is also examined.İçindekiler
ÖZET i
ABSTRACT ii
TEŞEKKUR iii
İÇİNDEKİLER DİZİNİ iv
SİMGELER VE KISALTMALAR DİZİNİ vi
1 GİRİŞ 1
2 TEMEL TANIM VE KAVRAMLAR 5
2.1 Temel Halka ve Modül Terimleri . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Değişmeli Halkalarda Asal İdealler . . . . . . . . . . . . . . . . . . . . . 9
2.3 Sonluluk Koşulları . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Krull Boyut Ve Kritik Modüller . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Ore Kümeler, Klasik Kesirler Halkası ve Goldie Teoremi . . . . . . . . . 16
2.6 Yoğun ve Monoform Modüller . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 Gabriel Filtreleri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 DEĞİŞMELİ HALKALAR 24
3.1 Değişmeli Halkalarda Cohen ve Kaplansky Teoremleri . . . . . . . . . . 24
3.2 S-Noether Halkalar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 TEK YÖNLÜ ASAL İDEAL PRENSİBİ 31
4.1 Tamamen Asal Sağ İdealler . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Tamamen Asal İdeal Prensibi . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Oka Aileleri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 Tamamen Asal İdeal Prensibinin Bazı Uygulamaları . . . . . . . . . . . 52
4.5 Comonoform Sağ İdealler İçin Asal İdeal Prensibi . . . . . . . . . . . . 62
5 OKA AİLELERİ YAKLAŞIMIYLA COHEN VE KAPLANSKY TEOREMLERİNİN
GENELLEMELERİ 71
5.1 Nokta Sıfırlayıcı Kümeler . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 Nokta Sıfırlayıcı Küme Teoremi ve Cohen Teoremi . . . . . . . . . . . . 79
5.3 Kaplansky-Cohen Teoremi . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.4 Dik Toplanan Altında Kapalı Aileler . . . . . . . . . . . . . . . . . . . 92
5.5 Kaplansky Teoremi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6 FARKLI YAKLAŞIMLARLA COHEN VE KAPLANSKY TEOREMLERİNİN
GENELLEMELERİ 103
6.1 Koh ve Chandran Yaklaşımı . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Michler Yaklaşımı . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.3 Tam Sınırlı Halkalar ve Cohen Teoremi . . . . . . . . . . . . . . . . . . 113
6.4 Değişmeli Olmayan S-Noether Halkalar . . . . . . . . . . . . . . . . . . 114
7 SONUÇLAR 120
KAYNAKLAR 123Değişmeli halka teorisinde, bir halkanın yapısının belirlenmesinde asal idealler oldukça
önemli araçlardır. Bu tez çalışmasında, yapı teoremlerinden Cohen ve Kaplansky’ye ait
teoremler ele alınacaktır. Tezin amacı, özellikle Reyes’in 2010 ve 2012 yıllarında yaptığı çalışmaları dikkate alarak Cohen ve Kaplansky Teoremleri’nin değişmeli olmayan halkalardaki
genellemelerini incelemektir. Giriş bölümünde, tez konusunun tarihsel gelişimi
ve halka teorisindeki önemi açıklanmaktadır. İkinci bölüm, tez için gerekli olan temel
bilgileri içermektedir. Üçüncü bölümde, Cohen ve Kaplansky Teoremleri’nin değişmeli
halkalardaki rolleri üzerinde durulmuştur. Ayrıca, Anderson ve Dumitrescu’nun üzerinde
çalıştığı S-Noether halka yapısı tanıtılmış ve bu halka sınıfının bazı özelliklerinden
bahsedilmiştir. Dördüncü bölümde, asal ideallerin değişmeli olmayan halkalardaki
tek yönlü genellemesi üzerinde durulmuş ve tamamen asal sağ idealler ve Oka
aileleri gibi bazı kavramlar tanıtılmıştır. Bu kavramların değişmeli olmayan bir halka
yapısını belirlemedeki rolü uygulamalı olarak incelenmiştir. Beşinci bölüm, Cohen ve
Kaplansky Teoremleri’nin Oka aileleri ve nokta sıfırlayıcı kümeler yardımıyla elde edilen
değişmeli olmayan halkalardaki genellemelerini içermektedir. Son bölümde ise Cohen
ve Kaplansky Teoremleri’nin farklı yaklaşımlarla elde edilen genellemeleri üzerinde durulmuştur.
Koh, Chandran ve Michler tarafından ele alınan genellemelerin yanı sıra
S-Noether halka yapısının değişmeli olmayan halkalardaki genellemesi incelenmiştir
Cellular distribution of LAPTM5.
No full text<p>Transfected M10 cells co-expressing EYFP-LAPTM5 and CD1e were fixed, permeabilized and co-stained with the anti-CD1e mAb 20.6, revealed using Cy3-conjugated antibodies (A) and antibodies specific for TGN46, revealed by Cy5-conjugated antibodies (B, left panel, represented using red pseudo-color), or stained with anti-EEA1, -CD63, -Lamp1 (B) or -HLA-DR Abs (C). Untreated cells (upper panel) were compared with cells treated for 4 hours with bafilomycin (lower panel) (A). D) M10 cells co-expressing CD1e and EYFP-LAPTM5 were fixed and processed for immunolabeling of cryosections with 10 nm anti-GFP and 15 nm anti-CD1e conjugated gold particles. EYFP-LAPTM5 and CD1e were detected in the endoplasmic reticulum (ER), in Golgi compartments (Golgi) and in multivesicular (MVs) and multilamellar endosomes (MLs). E, F) Characterization of two anti-LAPTM5 mAbs. M10 cells co-expressing CD1e and EYFP-LAPTM5 were fixed, permeabilized and stained with an anti-LAPTM5 mAb (2.16.1 or 47.15.6), which was revealed with Cy3-conjugated secondary Abs (E). M10 cells expressing CD1e were fixed, permeabilized and double-labeled with 2.16.1 and either anti-TGN46, anti-EEA1, anti-CD63 (H5C6) or anti-HLA-DR (L243) Abs (F). Scale bars, confocal micrographs, 10 µM; electron microscopy micrographs, 100 nM.</p
Learning from Internal Change Academy processes
No full textA 2007/8 Research and Development Grant from SEDA under its Supporting and Leading Educational Change programme provided Sheffield Hallam University with the opportunity to undertake an extremely interesting and timely piece of work on learning from Internal Change Academy processes. A presentation to the SEDA Spring Conference 2009 focused on understanding the value of Internal Change Academies as a model for leading educational change and demonstrated how a simple benchmarking exercise may provide a rich source of data in leading change processes. This article focuses on the broader lessons learnt about change rather than on the practicalities and the different models of running an Internal Change Academy. That information is available in the project final report (Flint and Oxley, 2009)
Uniform and staggered magnetizations induced by Dzyaloshinskii-Moriya interactions in isolated and coupled spin 1/2 dimers in a magnetic field
No full textInternational audienceWe investigate the interplay of Dzyaloshinskii-Moriya interactions and an external field in spin 1/2 dimers. For isolated dimers and at low field, we derive simple expressions for the staggered and uniform magnetizations which show that the orientation of the uniform magnetization can deviate significantly from that of the external field. In fact, in the limit where the vector of the Dzyaloshinskii-Moriya interaction is parallel to the external field, the uniform magnetization actually becomes {\it perpendicular} to the field. For larger fields, we show that the staggered magnetization of an isolated dimer has a maximum close to one-half the polarization, with a large maximal value of in the limit of very small Dzyaloshinskii-Moriya interaction. We investigate the effect of inter-dimer coupling in the context of ladders with Density Matrix Renormalization Group (DMRG) calculations and show that, as long as the values of the Dzyaloshinskii-Moriya and of the exchange interaction are compatible with respect to the development of a staggered magnetization, the simple picture that emerges for isolated dimers is also valid for weakly coupled dimers with minor modifications. The results are compared with torque measurements on Cu(CHN)Cl
To what extent do education and physical work load factors explain occupational differences in disability retirement due to knee OA? A nationwide register-based study in Finland
No full textObjectives To examine the association of education and physical work load factors on the occupational differences in disability retirement due to knee osteoarthritis (OA). Design Longitudinal study. Setting Linkage of several nationwide registers and a job exposure matrix in Finland. Participants A total of 1 135 654 Finns aged 30-60 years in gainful employment were followed from 2005 to 2013 for full disability retirement due to knee OA. Primary and secondary outcome measures We calculated age-adjusted incidence rates and examined the association of occupation, education and physical work load factors with disability retirement using competing risk regression model. Disability retirement due to other causes than knee OA, old-age retirement and death were treated as competing risk. Results A total of 6117 persons had disability retirement due to knee OA. Women had a higher age-adjusted incidence rate than men (72 vs 60 per 100000 person-years, respectively). In men, a very high risk of disability retirement was found among construction workers, electricians and plumbers (HR 16.6, 95%CI 12.5 to 22.2), service workers (HR 12.7, 95%CI 9.2 to 17.4) and in women among building caretakers, cleaners, assistant nurses and kitchen workers (HR 15.5, 95%CI 11.7 to 20.6), as compared with professionals. The observed occupational differences were largely explained by educational level and noticeably mediated by physical work load factors in both genders. Conclusion Our observational study suggests that the risk of disability retirement among manual workers is strongly attributed to the physically heavy work.Peer reviewe
Mating frequency of virgin and mated females.
No full text<p>Occurrence of copula in <i>L. longipalpis</i> for virgin (1° copula) and mated (2° copula) females. A single pair (1 male - 1 female) was used in each trial. X<sup>2</sup> = 10.071 and p<0.01.</p
General aspect of the <i>L. longipalpis</i> male reproductive system and the testes.
No full text<p><b>A)</b> SEM of an isolated male reproductive system, showing the pair of testes (Te), the <i>vasa deferentia</i> (VD), the seminal vesicle (SV), the ejaculatory duct (ED), the ejaculatory pump (EP) and the external genitalia or terminalia (TN). Also note the rectum (R). <b>B)</b> Light microscopy (LM) section showing the localization of the reproductive organs in the abdomen. Testes (Te) and the seminal vesicle (SV) are located in the fifth abdominal segment (V). Note pheromone gland cells (PG) in the fourth tergite (IV), and the ejaculatory pump (EP) in the sixth abdominal segment (VI). Note the well-developed fat body (FB) surrounding the testis and the seminal vesicle. <b>C)</b> LM section of a testis (Te) showing the organization of germ cells with different stages of development along the testis. Note the proximity of Malpighi tubules (MT) and the fat body (FB). <b>D)</b> Transmission electron microscopy (TEM) of germ cells (GC) and spermatozoa (Sp) surrounded by cystocytes (Cy), forming the cyst. In the spermatozoa, note the axoneme (arrow) lacking the central pair of microtubules and the mitochondria (Mi) close to it; N: nucleus of the cystocytes.</p
