Some aspects of Zariski topology for multiplication modules and their attached frames and quantales
For a multiplication R-module M we consider the Zariski topology in the set Spec (M) 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 (M). We also consider some topological aspec...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | México |
| Institución: | Universidad Autónoma de Ciudad Juárez |
| Repositorio: | Repositorio Institucional de la Universidad Autónoma de Ciudad Juárez |
| OAI Identifier: | oai:uacj.mx:oai:cathi.uacj.mx:20.500.11961ir-9780 |
| Acceso en línea: | https://doi.org/10.4134/JKMS.j180649 |
| Access Level: | acceso abierto |
| Palabra clave: | Multiplication modules Frames Quantales Zariski topology info:eu-repo/classification/cti/1 |
| Sumario: | For a multiplication R-module M we consider the Zariski topology in the set Spec (M) 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 (M). 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 (M/N) 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 ↑(N) Semp(M) = {P ∈ Semp (M) | N ⊆ P} and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M |
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