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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.
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.
Gonzalez-Cantu, Cynthia Minerva,Moreno-Pena, Pablo Juan,Salazar-Lara, Mayela Guadalupe,Garcia, Pablo Patricio Flores,Montes-Tapia, Fernando Felix,Cervantes-Kardasch, Victor Hugo,Castro-Govea, Yanko Korean Society of Plastic and Reconstructive Surge 2021 Archives of Plastic Surgery Vol.48 No.5
Epignathus is a rare congenital orofacial teratoma that arises from the sphenoid region of the palate or the pharynx. It occurs in approximately 1:35,000 to 1:200,000 live births representing 2% to 9% of all teratomas. We present the case of a newborn of 39.4 weeks of gestation with a tumor that occupied the entire oral cavity. The patient was delivered by cesarean section. Oral resection was managed by pediatric surgery. Plastic surgery used virtual 3-dimensional models to establish the extension, and depth of the tumor. Bloc resection and reconstruction of the epignathus were performed. The mass was diagnosed as a mature teratoma associated with cleft lip and palate, nasoethmoidal meningocele that conditions hypertelorism, and a pseudomacrostoma. Tridimensional technology was applied to plan the surgical intervention. It contributed to a better understanding of the relationships between the tumor and the adjacent structures. This optimized the surgical approach and outcome.