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 a...
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| Main Author: | |
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| Other Authors: | , |
| Format: | Artículo |
| Language: | en_US |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://doi.org/10.4134/JKMS.j180649 https://doi.org/10.4134/JKMS.j180649 |
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| Summary: | 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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