On split extensions of preordered groups (Q6062711)
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scientific article; zbMATH DE number 7761510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On split extensions of preordered groups |
scientific article; zbMATH DE number 7761510 |
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On split extensions of preordered groups (English)
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6 November 2023
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Summary: We investigate the behaviour of split extensions in the category \(\mathsf{OrdGrp}\) of (pre)ordered groups. Namely we show that the lexicographic order plays a key role on the existence of compatible orders for semidirect products, establishing necessary and sufficient conditions for such existence; we prove that the Split Short Five Lemma holds for (stably) strong split extensions, and identify classes of split extensions which admit a classifier.
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preordered group
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positive cone
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split extension
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\(S\)-protomodular category
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