Reduced submodules of finite dimensional polynomial modules

Let $k$ be a field with characteristic zero, $R$ be the ring $k[x_1, \cdots, x_n]$ and $I$ be a monomial ideal of $R$. We study the Artinian local algebra $R/I$ when considered as an $R$-module $M$. We show that the largest reduced submodule of $M$ coincides with both the socle of $M$ and the $k$-submodule of $M$ generated by all outside corner elements of the Young diagram associated with $M$. Interpretations of different reduced modules is given in terms of Macaulay inverse systems. It is further shown that these reduced submodules are examples of modules in a torsion-torsionfree class, together with their duals; coreduced modules, exhibit symmetries in regard to Matlis duality and torsion theories. Lastly, we show that any $R$-module $M$ of the kind described here satisfies the radical formula.Comment: 19 page

Residuation in the set of topologizing filters of a ring

Read abstract in the documentThesis (PhD)--University of Pretoria, 2016.Mathematics and Applied MathematicsPhDUnrestricte

Commutativity in the lattice of topologizing filters of a ring – localization and congruences

Please read abstract in the article.The National Research Foundation of South Africa under Grant Number UID 85784.http://link.springer.com/journal/104742020-04-01hj2019Mathematics and Applied Mathematic

Commutativity in the lattice of topologizing filters of a commutative semiartinian ring

Please read abstract in the article.The DST-NRF CoE-MaSS (South Africa), the ISP (International Science Program) and the National Research Foundation (NRF) of South Africa.https://www.tandfonline.com/loi/lagb202020-06-27hj2020Mathematics and Applied Mathematic

Proportion of stillbirth and associated factors among women who deliver at public hospitals in Bahir Dar city, north-West Ethiopia

Abstract Introduction The annual global burden of stillbirths is estimated to be 3.2 million, of which 98% occur in low and middle-income countries (LMICs). In the Amhara region of Ethiopia, the prevalence of stillbirth outcomes was 85 per 1000. Ethiopia is experiencing an increase in the number of health professionals attending deliveries, however, stillbirth rates are not decreasing as anticipated. However, there are limited numbers of studies done related to the proportion of stillbirths and associated factors in the study area. This study aimed to assess the proportion of stillbirths and associated factors among women who attended deliveries at Tibebe Ghion Specialized Hospital and Felege Hiwot Comprehensive Specialized Hospital. Methods An institutional-based cross-sectional study was conducted on 366 women who delivered at two referral hospitals in Bahir Dar from April 1, 2020, to August 30, 2020. Study participants were selected using systematic random sampling techniques. A checklist and structured questionnaire were used to retrieve information from the clients and their attendants. The collected data were cleaned, coded, and entered into Epi-data version 3.1 and then exported into SPSS 23 for analysis. Bivariate and multivariable logistic regression analysis was computed to identify statistically significant associated factors with a P value < 0.05. The results were presented in tables and charts. Result The proportion of stillbirths was 3.8% in this study area. This study showed that level of education, who completed primary school (AOR = 0.12; 95% CI (0.01, 0.98)), not using partograph (AOR = 3.77, 95%; CI (1.02; 13.93)), and obstetric complication (AOR = 6.7; 95% CI (1.54, 29.79) were the major factors affecting the stillbirth. Conclusion Our study found that stillbirth rate remains a major public health problem. Illiteracy, not using a partograph, and having obstetric complications were major associated factors for stillbirth. The risk factors identified in this study can be prevented and managed by providing appropriate care during preconception, antepartum, and intrapartum periods