Geometry of Autometrized Lattice Ordered Monoids
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929232633921536 |
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| author | Ashale, Tekalign Regasa Abebe, Girum Aklilu Venkateswarlu, Kolluru |
| author_facet | Ashale, Tekalign Regasa Abebe, Girum Aklilu Venkateswarlu, Kolluru |
| contents | In this paper, we study the geometry of AL-monoids by introducing the concept of metric betweeness and its properties t1, t2,, B-linearity, D-linearity, lattice betweeness, B-linearity, and Dlinearity, segments and equilateral triangles. It is proved that there do not exist equilateral triangles in AL-monoids. It is also proved that any AL-monoid is ptolemaic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01907 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry of Autometrized Lattice Ordered Monoids Ashale, Tekalign Regasa Abebe, Girum Aklilu Venkateswarlu, Kolluru Logic 47H09, 47H10 In this paper, we study the geometry of AL-monoids by introducing the concept of metric betweeness and its properties t1, t2,, B-linearity, D-linearity, lattice betweeness, B-linearity, and Dlinearity, segments and equilateral triangles. It is proved that there do not exist equilateral triangles in AL-monoids. It is also proved that any AL-monoid is ptolemaic. |
| title | Geometry of Autometrized Lattice Ordered Monoids |
| topic | Logic 47H09, 47H10 |
| url | https://arxiv.org/abs/2402.01907 |