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A generalization of multiplication modules
Jaime Castro Perez,Jose Rios Montes,Gustavo Tapia Sanchez 대한수학회 2019 대한수학회보 Vol.56 No.1
For $M\in R$-Mod, $N\subseteq M$ and $L\in \sigma \left[ M \right] $ we consider the product $N_{M}L=\sum_{f\in {\rm Hom}_{R} ( M,L ) }f ( N ) $. A module $N\in \sigma \left[ M\right] $ is called an $M$-multiplication module if for every submodule $L$ of $N$, there exists a submodule $I$ of $M$ such that $L=I_{M}N$. We extend some important results given for multiplication modules to $M$-multiplication modules. As applications we obtain some new results when $M$ is a semiprime Goldie module. In particular we prove that $M$ is a semiprime Goldie module with an essential socle and $N$ $\in \sigma \left[ M\right] $ is an $M$ -multiplication module, then $N$ is cyclic, distributive and semisimple module. To prove these results we have had to develop new methods.
Some aspects of Zariski topology for multiplication modules and their attached frames and quantales
Jaime Castro Perez,Jose Rios,Gustavo Tapia Sanchez 대한수학회 2019 대한수학회지 Vol.56 No.5
For a multiplication $R$-module $M$ we consider the Zariski topology in the set $Spec\left( M\right) $ of prime submodules of $M$. We investigate the relationship between the algebraic properties of the submodules of $M$ and the topological properties of some subspaces of $Spec\left( M\right) $. We also consider some topological aspects of certain frames. We prove that if $ R $ is a commutative ring and $M$ is a multiplication $R$-module, then the lattice $Semp\left( M/N\right) $ of semiprime submodules of $M/N$ is a spatial frame for every submodule $N$ of $M$. When $M$ is a quasi projective module, we obtain that the interval $\mathcal{\uparrow } (N)^{Semp\left( M\right) }=\left\{ P\in Semp\left( M\right) \mid N\subseteq P\right\} $ and the lattice $Semp\left( M/N\right) $ are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of $M$.
A GENERALIZATION OF MULTIPLICATION MODULES
Perez, Jaime Castro,Montes, Jose Rios,Sanchez, Gustavo Tapia Korean Mathematical Society 2019 대한수학회보 Vol.56 No.1
For $M{\in}R-Mod$, $N{\subseteq}M$ and $L{\in}{\sigma}[M]$ we consider the product $N_ML={\sum}_{f{\in}Hom_R(M,L)}\;f(N)$. A module $N{\in}{\sigma}[M]$ is called an M-multiplication module if for every submodule L of N, there exists a submodule I of M such that $L=I_MN$. We extend some important results given for multiplication modules to M-multiplication modules. As applications we obtain some new results when M is a semiprime Goldie module. In particular we prove that M is a semiprime Goldie module with an essential socle and $N{\in}{\sigma}[M]$ is an M-multiplication module, then N is cyclic, distributive and semisimple module. To prove these results we have had to develop new methods.
Paola Perez,Jaime Patiño,Alexis A. Franco,Fernando Rosso,Estefania Beltran,Eliana Manzi,Andrés Castro,Mayra Estacio,Diego Medina Valencia 대한혈액학회 2022 Blood Research Vol.57 No.1
Background Antifungal prophylaxis is recommended for hematopoietic stem cell transplantation (HSCT) to decrease the incidence of invasive fungal infections (IFI). This study aimed to compare the two groups of antifungal prophylaxis in pediatric patients undergoing allogeneic HSCT. Methods This observational, analytic, retrospective cohort study compared the incidence of IFI with antifungal prophylaxis with voriconazole vs. other antifungals in the first 100 days after allogeneic HSCT in patients aged <18 years between 2012 and 2018. The statistical analysis included univariate and multivariate analyses and determination of the cumulative incidence of invasive fungal infection by the Kaplan‒Meier method using STATA 14 statistical software. Results A total of 139 allogeneic HSCT were performed. The principal diagnosis was acute leukemia (63%). The 75% had haploidentical donors, and 50% used an antifungal in the month before transplantation. Voriconazole (69%) was the most frequently administered antifungal prophylaxis. The cumulative incidence of IFI was 5% (7 cases). Of the patients with IFIs, four began prophylaxis with voriconazole, one with caspofungin, and one with fluconazole. Additionally, six were possible cases, one was proven (Candida parapsilosis), and 1/7 died. Conclusion There were no differences in the incidence of IFI between patients who received prophylaxis with voriconazole and other antifungal agents.