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RISS 인기검색어
- 검색키워드
- 저자 : Gustavo Tapia Sanchez (검색결과 3 건)
- 무료
- 기관 내 무료
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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.
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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 $M$.
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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.
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