Unitally nondistributive quantales
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909408201539584 |
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| author | García, Javier Gutiérrez Höhle, Ulrich |
| author_facet | García, Javier Gutiérrez Höhle, Ulrich |
| contents | Unitally nondistributive quantales are unital quantales such that the unit is approximable by the totally below relation and does not meet-distribute over arbitrary joins. It is shown that the underlying nondistributive complete lattice contains at least $7$ elements. Moreover, under mild conditions, every quantale has an extension to a unitally nondistributive quantale by the addition of an isolated unit. As a byproduct of this construction we prove that there exist $30$ non-isomorphic, unitally nondistributive quantales on the set of $7$ elements. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_17284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitally nondistributive quantales García, Javier Gutiérrez Höhle, Ulrich General Topology 2020: Primary 06F07 Secondary 06A06, 06B05 Unitally nondistributive quantales are unital quantales such that the unit is approximable by the totally below relation and does not meet-distribute over arbitrary joins. It is shown that the underlying nondistributive complete lattice contains at least $7$ elements. Moreover, under mild conditions, every quantale has an extension to a unitally nondistributive quantale by the addition of an isolated unit. As a byproduct of this construction we prove that there exist $30$ non-isomorphic, unitally nondistributive quantales on the set of $7$ elements. |
| title | Unitally nondistributive quantales |
| topic | General Topology 2020: Primary 06F07 Secondary 06A06, 06B05 |
| url | https://arxiv.org/abs/2402.17284 |