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Main Author: Jokela, Jani
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2502.13235
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author Jokela, Jani
author_facet Jokela, Jani
contents A mixed lattice is a partially ordered set with two mixed partial orderings that are linked by asymmetric upper and lower envelopes. These notions generalize the join and meet operations of a lattice. In the present paper, we study different types of partially ordered semigroups with two mixed orderings, and investigate their relationship to subsemigroups of mixed lattice groups, which are partially ordered groups with a similar order structure. We also consider Archimedean orderings, and we show that elements of finite order cannot exist in a rather general class of Archimedean mixed lattice groups. Moreover, we give an example of a non-Archimedean mixed lattice group that contains an element of finite order.
format Preprint
id arxiv_https___arxiv_org_abs_2502_13235
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Partially ordered semigroups and groups with two mixed partial orderings
Jokela, Jani
Group Theory
Functional Analysis
06F20
A mixed lattice is a partially ordered set with two mixed partial orderings that are linked by asymmetric upper and lower envelopes. These notions generalize the join and meet operations of a lattice. In the present paper, we study different types of partially ordered semigroups with two mixed orderings, and investigate their relationship to subsemigroups of mixed lattice groups, which are partially ordered groups with a similar order structure. We also consider Archimedean orderings, and we show that elements of finite order cannot exist in a rather general class of Archimedean mixed lattice groups. Moreover, we give an example of a non-Archimedean mixed lattice group that contains an element of finite order.
title Partially ordered semigroups and groups with two mixed partial orderings
topic Group Theory
Functional Analysis
06F20
url https://arxiv.org/abs/2502.13235