Let S = S[I;S_i,φ_(j,i)] be a strong semilattice of semigroups such that I is finite and each S_i (i∈ I) be a family of disjoint semigroups. In this article some finiteness conditions which are periodicity, local finiteness and locally finite presentability are considered for S. It is proven that a strong semilattice of semigroups S[I;S_i,φ_(j,i)] is periodic, locally finite, locally finitely presented and residually finite, respectively if and only if I is finite and each semigroup S_i (i∈ I) is periodic, locally finite, locally finitely presented and residually finite, respectively.
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机译：令S = S [I; S_i，φ_（j，i）]为半群的强半格，使得I是有限的，每个S_i（i∈I）为不相交半群的族。本文考虑了S的一些周期性，局部有限性和局部有限的可表示性。证明了半群S [I; S_i，φ_（j，i）]的强半格是周期性的，局部有限的，局部的当且仅当I是有限的并且每个半群S_i（i∈I）分别是周期性的，局部有限的，局部有限地表示的和残差有限的时，分别表示为有限表示和残差有限。
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