BORIS Theses

BORIS Theses
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Order, algebra, and structure: lattice-ordered groups and beyond

Colacito, Almudena (2020). Order, algebra, and structure: lattice-ordered groups and beyond. (Thesis). Universität Bern, Bern

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This thesis describes and examines some remarkable relationships existing between seemingly quite different properties (algebraic, order-theoretic, and structural) of ordered groups. On the one hand, it revisits the foundational aspects of the structure theory of lattice-ordered groups, contributing a novel systematization of its relationship with the theory of orderable groups. One of the main contributions in this direction is a connection between validity in varieties of lattice-ordered groups, and orders on groups; a framework is also provided that allows for a systematic account of the relationship between orders and preorders on groups, and the structure theory of lattice-ordered groups. On the other hand, it branches off in new directions, probing the frontiers of several different areas of current research. More specifically, one of the main goals of this thesis is to suitably extend results that are proper to the theory of lattice-ordered groups to the realm of more general, related algebraic structures; namely, distributive lattice-ordered monoids and residuated lattices. The theory of lattice-ordered groups provides themain source of inspiration for this thesis’ contributions on these topics.

Item Type: Thesis
Dissertation Type: Single
Date of Defense: 8 July 2020
Subjects: 500 Science > 510 Mathematics
Institute / Center: 08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics
Depositing User: Hammer Igor
Date Deposited: 18 Sep 2020 06:48
Last Modified: 08 Jul 2021 00:30

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