Primary Ideals and Primary Modules over Noncommutative Rings

The concepts of prime ideals and prime modules were introduced over noncommutative rings. In this article we generalize these concepts and introduce the concepts of primary ideals and primary modules over noncommutative rings. Also we give equivalent definitions of primary ideals over noncommutative rings. Finally, we study some properties of primary submodules over noncommutative rings

Primary Rimary Finitely Compactly Packed Modules And Dauns-Primary Submodules Over Noncommutative Rings

In this paper we generalize the concept of primary finitely compactly packed modules over noncommutative rings. This concept generalizes the concepts of primary compactly packed modules over noncommutative rings, and primary finitely compactly packed modules over commutative rings. We first find the relation between primary finitely compactly packed modules and primary compactly packed modules over noncommutative rings. We also prove several results on the primary finitely compactly packed modules over noncommutative rings. In addition, we introduce the definition of Dauns-primary submodules over noncommutative rings, and investigate the relation between this concept and the concepts of Dauns-prime submodules, and primary submodules over noncommutative rings

On Primary Compactly Packed Modules over non commutative rings

This research considers three basic concepts concerning primary submodules, which are important, at least to some mathematicians. The first concept is the concept of primary radical of a submodule, the second concept is the concept of minimal primary submodules, and the third one is the concept of primary compactly packed modules. In this paper, we generalize these three concepts over noncommutative rings and generalize many results concerning them, in the rings that are not necessary commutative

On Weakly Almost Generalized 2-Absorbing Sub-modules of Modules

Let M be a module over a commutative ring R with non-zero identity. A proper sub-module N of M is called weakly almost generalized 2-absorbing (denoted by WAG2 -absorbing) sub-module, if for  and with  either  or  or  for some positive integers  and . We study the relation between WAG2 -absorbing sub-modules and primary, weak primary and weakly primary sub-modules. Also, we study the behavior of , when N is WAG2 -absorbing sub-module. Moreover, the WAG2 -absorbing sub-modules when  are characterized

Antimicrobial resistance among migrants in Europe: a systematic review and meta-analysis

BACKGROUND: Rates of antimicrobial resistance (AMR) are rising globally and there is concern that increased migration is contributing to the burden of antibiotic resistance in Europe. However, the effect of migration on the burden of AMR in Europe has not yet been comprehensively examined. Therefore, we did a systematic review and meta-analysis to identify and synthesise data for AMR carriage or infection in migrants to Europe to examine differences in patterns of AMR across migrant groups and in different settings. METHODS: For this systematic review and meta-analysis, we searched MEDLINE, Embase, PubMed, and Scopus with no language restrictions from Jan 1, 2000, to Jan 18, 2017, for primary data from observational studies reporting antibacterial resistance in common bacterial pathogens among migrants to 21 European Union-15 and European Economic Area countries. To be eligible for inclusion, studies had to report data on carriage or infection with laboratory-confirmed antibiotic-resistant organisms in migrant populations. We extracted data from eligible studies and assessed quality using piloted, standardised forms. We did not examine drug resistance in tuberculosis and excluded articles solely reporting on this parameter. We also excluded articles in which migrant status was determined by ethnicity, country of birth of participants' parents, or was not defined, and articles in which data were not disaggregated by migrant status. Outcomes were carriage of or infection with antibiotic-resistant organisms. We used random-effects models to calculate the pooled prevalence of each outcome. The study protocol is registered with PROSPERO, number CRD42016043681. FINDINGS: We identified 2274 articles, of which 23 observational studies reporting on antibiotic resistance in 2319 migrants were included. The pooled prevalence of any AMR carriage or AMR infection in migrants was 25·4% (95% CI 19·1-31·8; I2 =98%), including meticillin-resistant Staphylococcus aureus (7·8%, 4·8-10·7; I2 =92%) and antibiotic-resistant Gram-negative bacteria (27·2%, 17·6-36·8; I2 =94%). The pooled prevalence of any AMR carriage or infection was higher in refugees and asylum seekers (33·0%, 18·3-47·6; I2 =98%) than in other migrant groups (6·6%, 1·8-11·3; I2 =92%). The pooled prevalence of antibiotic-resistant organisms was slightly higher in high-migrant community settings (33·1%, 11·1-55·1; I2 =96%) than in migrants in hospitals (24·3%, 16·1-32·6; I2 =98%). We did not find evidence of high rates of transmission of AMR from migrant to host populations. INTERPRETATION: Migrants are exposed to conditions favouring the emergence of drug resistance during transit and in host countries in Europe. Increased antibiotic resistance among refugees and asylum seekers and in high-migrant community settings (such as refugee camps and detention facilities) highlights the need for improved living conditions, access to health care, and initiatives to facilitate detection of and appropriate high-quality treatment for antibiotic-resistant infections during transit and in host countries. Protocols for the prevention and control of infection and for antibiotic surveillance need to be integrated in all aspects of health care, which should be accessible for all migrant groups, and should target determinants of AMR before, during, and after migration. FUNDING: UK National Institute for Health Research Imperial Biomedical Research Centre, Imperial College Healthcare Charity, the Wellcome Trust, and UK National Institute for Health Research Health Protection Research Unit in Healthcare-associated Infections and Antimictobial Resistance at Imperial College London

Surgical site infection after gastrointestinal surgery in high-income, middle-income, and low-income countries: a prospective, international, multicentre cohort study

Background: Surgical site infection (SSI) is one of the most common infections associated with health care, but its importance as a global health priority is not fully understood. We quantified the burden of SSI after gastrointestinal surgery in countries in all parts of the world. Methods: This international, prospective, multicentre cohort study included consecutive patients undergoing elective or emergency gastrointestinal resection within 2-week time periods at any health-care facility in any country. Countries with participating centres were stratified into high-income, middle-income, and low-income groups according to the UN's Human Development Index (HDI). Data variables from the GlobalSurg 1 study and other studies that have been found to affect the likelihood of SSI were entered into risk adjustment models. The primary outcome measure was the 30-day SSI incidence (defined by US Centers for Disease Control and Prevention criteria for superficial and deep incisional SSI). Relationships with explanatory variables were examined using Bayesian multilevel logistic regression models. This trial is registered with ClinicalTrials.gov, number NCT02662231. Findings: Between Jan 4, 2016, and July 31, 2016, 13 265 records were submitted for analysis. 12 539 patients from 343 hospitals in 66 countries were included. 7339 (58·5%) patient were from high-HDI countries (193 hospitals in 30 countries), 3918 (31·2%) patients were from middle-HDI countries (82 hospitals in 18 countries), and 1282 (10·2%) patients were from low-HDI countries (68 hospitals in 18 countries). In total, 1538 (12·3%) patients had SSI within 30 days of surgery. The incidence of SSI varied between countries with high (691 [9·4%] of 7339 patients), middle (549 [14·0%] of 3918 patients), and low (298 [23·2%] of 1282) HDI (p < 0·001). The highest SSI incidence in each HDI group was after dirty surgery (102 [17·8%] of 574 patients in high-HDI countries; 74 [31·4%] of 236 patients in middle-HDI countries; 72 [39·8%] of 181 patients in low-HDI countries). Following risk factor adjustment, patients in low-HDI countries were at greatest risk of SSI (adjusted odds ratio 1·60, 95% credible interval 1·05–2·37; p=0·030). 132 (21·6%) of 610 patients with an SSI and a microbiology culture result had an infection that was resistant to the prophylactic antibiotic used. Resistant infections were detected in 49 (16·6%) of 295 patients in high-HDI countries, in 37 (19·8%) of 187 patients in middle-HDI countries, and in 46 (35·9%) of 128 patients in low-HDI countries (p < 0·001). Interpretation: Countries with a low HDI carry a disproportionately greater burden of SSI than countries with a middle or high HDI and might have higher rates of antibiotic resistance. In view of WHO recommendations on SSI prevention that highlight the absence of high-quality interventional research, urgent, pragmatic, randomised trials based in LMICs are needed to assess measures aiming to reduce this preventable complication

المقاسات الابتدائية المنتهية المحزومة الرص و المقاسات الجزئية الابتدائية من النمط دونس المعرفة على الحلقات غير الابدالية

This research considers three basic concepts concerning primary submodules, which are important, at least to some mathematicians. The first concept is the concept of primary radical of a submodule, the second concept is the concept of minimal primary submodules, and the third one is the concept of primary compactly packed modules. In this paper, we generalize these three concepts over noncommutative rings and generalize many results concerning them, in the rings that are not necessary commutative. : . . . .نعمم في هذا البحث مفهوم المقاسات المنتهية المحزومة الرص على الحلقات غير الابدالية . حيث أن هذا المفهوم هو تعميم لمفهومي المقاسات المحزومة الرص على الحلقات غير الابدالية و المقاسات المنتهية المحزومة الرص على الحلقات الابدالية. في البداية نجد العلاقة بين المقاسات المنتهية المحزومة الرص و المقاسات المحزومة الرص على الحلقات الغير ابدالية, ثم نبرهن بعض النتائج المتعلقة بالمقاسات المنتهية المحزومة الرص على الحلقات غير الابدالية. ونطرح في النهاية مفهوم المقاسات الجزئية الابتدائية من النمط دونس المعرفة على الحلقات غير الابدالية, ونجد العلاقة بينها و بين المقاسات الجزئية الأولية من النمط دونس و المقاسات الجزئية الابتدائية المعرفة على الحلقات غير الابدالية

المثاليات والمقاسات الإبتدائية المعرفة على الحلقات غير الإبدالية

The concepts of prime ideals and prime modules were introduced over noncommutative rings. In this article we generalize these concepts and introduce the concepts of primary ideals and primary modules over noncommutative rings. Also we give equivalent definitions of primary ideals over noncommutative rings. Finally, we study some properties of primary submodules over noncommutative rings. Key Words: Primary ideals over noncommutative rings, radical annihilator of an R-module, prime modules over noncommutative rings, primary modules over noncommutative rings, primary submodules over noncommutative rings.من المعروف أن المثاليات الإبتدائية والمقاسات الإبتدائية قد تم تعريفها على الحلقات الإبدالية.في هذا البحث تم تعريف المثاليات الإبتدائية والمقاسات الإبتدائية على الحلقات غير الإبدالية, وقد تم إثبات أن هذا التعريف هو تعميم لتعريف المثاليات الإبتدائية والمقاسات الإبتدائية على الحلقات الإبدالية, كذلك تم إثبات أنه تعميم لتعريف المثاليات الأولية والمقاسات الأولية على الحلقات الغير الإبدالية في نهاية بحثنا قمنا بدراسة بعض خواص المقاسات الجزئية الإبتدائية على الحلقات الغير الإبدالية

On n-primly ideals

An ideal I is primal over a commutative ring R with non zero identity if the set of all elements that are not prime to I, forms an ideal of R. This definition was introduced by Ladislas Fuchs in 1950. In this paper, we define an ideal I over a commutative ring R with non zero identity to be n-primly if the set of all elements that are not n-primary to I, forms an ideal of R. But first we introduced the concepts of n-primary elements to an ideal, n-adjoint sets for an ideal, uniformly not n-primary sets for an ideal, n-primly ideals and uniformly n-primly ideals. We study the previous concepts in details illustrated by several examples. We also study the relation between several sets like n-adjoint sets for an ideal, n-adjoint sets for an ideal and the adjoint set for this ideal, sets that are not n-primary for an ideal and uniformly not n-primary sets for this ideal. Also we investigate the relation between some ideals like uniformly n-primly ideals and n-primly ideals, primary ideals and n-primly ideals over a commutative ring with identit

On weakly primary submodules

Let R be a commutative ring with non-zero identity. A proper submodule N of an R-module M is weakly primary i