Properties of a certain product of submodules

Let R be a commutative ring with identity, M an R-module and K1, . . . , Kn submodules of M. In this article, we construct an algebraic object, called product of K1, . . . , Kn. We equipped this structure with appropriate operations to get an R(M)-module. It is shown that R(M)-module Mⁿ = M . . . M and R-module M inherit some of the most important properties of each other. For example, we show that M is a projective (flat) R-module if and only if Mⁿ is a projective (flat) R(M)-moduleПрипустимо, що R — комутативне кiльце з одиницею, M — R-модуль i K1, . . . , Kn — пiдмодулi M. Побудовано алгебраїчний об’єкт, що називається добутком пiдмодулiв K1, . . . , Kn. Цю структуру оснащено вiдповiдними операцiями для отримання R(M)-модуля. Показано, що R(M)-модуль Mⁿ = M . . . M та R-модуль M успадковують деякi з найбiльш важливих властивостей один одного. Наприклад, показано, що M є проективним (плоским) R-модулем тодi i тiльки тодi, коли Mⁿ — проективний (плоский) R(M)-модуль

Strong resolving graph of the intersection graph in commutative rings

The intersection graph of ideals associated with a commutative unitary ring $R$ is the graph $G(R)$ whose vertices all non-trivial ideals of $R$ and there exists an edge between distinct vertices if and only if the intersection of them is non-zero. In this paper, the structure of the resolving graph of $G(R)$ is characterized and as an application, we evaluate the strong metric dimension of $G(R)$.Comment: arXiv admin note: substantial text overlap with arXiv:2308.0969

On the inclusion ideal graph of a poset

Let (P,≤) be an atomic partially ordered set (poset, briefly) with a minimum element 0 and \u1d57f(P) the set of nontrivial ideals of P. The inclusion ideal graph of P, denoted by Ω(P), is an undirected and simple graph with the vertex set \u1d57f(P) and two distinct vertices I, J ∈ \u1d57f(P) are adjacent in Ω(P) if and only if I ⊂ J or J ⊂ I. We study some connections between the graph theoretic properties of this graph and some algebraic properties of a poset. We prove that Ω(P) is not connected if and only if P = {0, a1, a2}, where a1, a2 are two atoms. Moreover, it is shown that if Ω(P) is connected, then diam(Ω(P)) ≤ 3. Also, we show that if Ω(P) contains a cycle, then girth(Ω(P)) ∈ {3, 6}. Furthermore, all posets based on their diameters and girths of inclusion ideal graphs are characterized. Among other results, all posets whose inclusion ideal graphs are path, cycle and star are characterized

The clinical relevance of oliguria in the critically ill patient : Analysis of a large observational database

Funding Information: Marc Leone reports receiving consulting fees from Amomed and Aguettant; lecture fees from MSD, Pfizer, Octapharma, 3 M, Aspen, Orion; travel support from LFB; and grant support from PHRC IR and his institution. JLV is the Editor-in-Chief of Critical Care. The other authors declare that they have no relevant financial interests. Publisher Copyright: © 2020 The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.Background: Urine output is widely used as one of the criteria for the diagnosis and staging of acute renal failure, but few studies have specifically assessed the role of oliguria as a marker of acute renal failure or outcomes in general intensive care unit (ICU) patients. Using a large multinational database, we therefore evaluated the occurrence of oliguria (defined as a urine output 16 years) patients in the ICON audit who had a urine output measurement on the day of admission were included. To investigate the association between oliguria and mortality, we used a multilevel analysis. Results: Of the 8292 patients included, 2050 (24.7%) were oliguric during the first 24 h of admission. Patients with oliguria on admission who had at least one additional 24-h urine output recorded during their ICU stay (n = 1349) were divided into three groups: transient - oliguria resolved within 48 h after the admission day (n = 390 [28.9%]), prolonged - oliguria resolved > 48 h after the admission day (n = 141 [10.5%]), and permanent - oliguria persisting for the whole ICU stay or again present at the end of the ICU stay (n = 818 [60.6%]). ICU and hospital mortality rates were higher in patients with oliguria than in those without, except for patients with transient oliguria who had significantly lower mortality rates than non-oliguric patients. In multilevel analysis, the need for RRT was associated with a significantly higher risk of death (OR = 1.51 [95% CI 1.19-1.91], p = 0.001), but the presence of oliguria on admission was not (OR = 1.14 [95% CI 0.97-1.34], p = 0.103). Conclusions: Oliguria is common in ICU patients and may have a relatively benign nature if only transient. The duration of oliguria and need for RRT are associated with worse outcome.publishersversionPeer reviewe

Epidemiology of intra-abdominal infection and sepsis in critically ill patients: “AbSeS”, a multinational observational cohort study and ESICM Trials Group Project

Purpose: To describe the epidemiology of intra-abdominal infection in an international cohort of ICU patients according to a new system that classifies cases according to setting of infection acquisition (community-acquired, early onset hospital-acquired, and late-onset hospital-acquired), anatomical disruption (absent or present with localized or diffuse peritonitis), and severity of disease expression (infection, sepsis, and septic shock). Methods: We performed a multicenter (n = 309), observational, epidemiological study including adult ICU patients diagnosed with intra-abdominal infection. Risk factors for mortality were assessed by logistic regression analysis. Results: The cohort included 2621 patients. Setting of infection acquisition was community-acquired in 31.6%, early onset hospital-acquired in 25%, and late-onset hospital-acquired in 43.4% of patients. Overall prevalence of antimicrobial resistance was 26.3% and difficult-to-treat resistant Gram-negative bacteria 4.3%, with great variation according to geographic region. No difference in prevalence of antimicrobial resistance was observed according to setting of infection acquisition. Overall mortality was 29.1%. Independent risk factors for mortality included late-onset hospital-acquired infection, diffuse peritonitis, sepsis, septic shock, older age, malnutrition, liver failure, congestive heart failure, antimicrobial resistance (either methicillin-resistant Staphylococcus aureus, vancomycin-resistant enterococci, extended-spectrum beta-lactamase-producing Gram-negative bacteria, or carbapenem-resistant Gram-negative bacteria) and source control failure evidenced by either the need for surgical revision or persistent inflammation. Conclusion: This multinational, heterogeneous cohort of ICU patients with intra-abdominal infection revealed that setting of infection acquisition, anatomical disruption, and severity of disease expression are disease-specific phenotypic characteristics associated with outcome, irrespective of the type of infection. Antimicrobial resistance is equally common in community-acquired as in hospital-acquired infection

Antimicrobial de-escalation in the critically ill patient and assessment of clinical cure: the DIANA study

Purpose: The DIANA study aimed to evaluate how often antimicrobial de-escalation (ADE) of empirical treatment is performed in the intensive care unit (ICU) and to estimate the effect of ADE on clinical cure on day 7 following treatment initiation. Methods: Adult ICU patients receiving empirical antimicrobial therapy for bacterial infection were studied in a prospective observational study from October 2016 until May 2018. ADE was defined as (1) discontinuation of an antimicrobial in case of empirical combination therapy or (2) replacement of an antimicrobial with the intention to narrow the antimicrobial spectrum, within the first 3 days of therapy. Inverse probability (IP) weighting was used to account for time-varying confounding when estimating the effect of ADE on clinical cure. Results: Overall, 1495 patients from 152 ICUs in 28 countries were studied. Combination therapy was prescribed in 50%, and carbapenems were prescribed in 26% of patients. Empirical therapy underwent ADE, no change and change other than ADE within the first 3 days in 16%, 63% and 22%, respectively. Unadjusted mortality at day 28 was 15.8% in the ADE cohort and 19.4% in patients with no change [p = 0.27; RR 0.83 (95% CI 0.60\u20131.14)]. The IP-weighted relative risk estimate for clinical cure comparing ADE with no-ADE patients (no change or change other than ADE) was 1.37 (95% CI 1.14\u20131.64). Conclusion: ADE was infrequently applied in critically ill-infected patients. The observational effect estimate on clinical cure suggested no deleterious impact of ADE compared to no-ADE. However, residual confounding is likely

Nurses' perceptions of aids and obstacles to the provision of optimal end of life care in ICU

Contains fulltext : 172380.pdf (publisher's version ) (Open Access

On the metric dimension of strongly annihilating-ideal graphs of commutative rings

Let be a commutative ring with identity and () be the set of ideals with non-zero annihilator. The strongly annihilating-ideal graph of is defined as the graph SAG() with the vertex set ()* = () \{0} and two distinct vertices I and J are adjacent if and only if I ∩ Ann(J) ≠ (0) and J ∩ Ann(I) ≠ (0). In this paper, we study the metric dimension of SAG() and some metric dimension formulae for strongly annihilating-ideal graphs are given