Some classes of directoid groups

• Date: 2018
• Main Authors: Gardner, B. J., Parmenter, M. M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: directoid; directed abelian group; variety; 06F20; 08B99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/768
• Journal Title: Algebra and Discrete Mathematics

Directoid groups are 2-torsion-free abelian groups with an extra binary operation assigning upper bounds. They thus constitute a generalization of abelian \(l\)-groups and an equational substitute for directed abelian groups. We discuss some classes of directoid groups, including varieties.