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On free \(\ell\)-semigroups. (Russian) Zbl 0582.06016
A (standard) construction of the free object F(X) over a set X in the variety of \(\ell\)-semigroups is given. Further, it is proved that the free \(\ell\)-semigroup F(X) over a countable set X can be embedded into a monogeneous free \(\ell\)-semigroup. As a corollary one obtains that the base rank of the variety of all \(\ell\)-semigroups equals 1.
Reviewer: V.Novák

MSC:
06F05 Ordered semigroups and monoids
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