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Directoid groups. (English) Zbl 1174.06340

Summary: We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.

MSC:

06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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References:

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