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Injective vector valued semigroups. (English) Zbl 1011.20067

The authors introduce the notion of injective vector valued semigroups. Then they show that the class of injective vector valued semigroups is larger than the class of free vector valued semigroups, and give a necessary and sufficient condition for injective vector valued semigroups to be free vector valued semigroups. All this gives a way for checking whether a given vector valued semigroup is free.

MSC:

20N15 \(n\)-ary systems \((n\ge 3)\)
20M99 Semigroups
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