Corrigendum to ``Perfect semilattices'' (Q1061757)

B. M. Schein let us know that \(S_ 3\) is not perfect. In fact, it is the smallest non-perfect semilattice. Consequently, Theorem 1 of the paper mentioned in the title [ibid. 32, 23-29 (1985; Zbl 0564.06004)] has to be corrected as follows. Let S be a semilattice. Then the following are equivalent: (1) S is perfect; (4) S is a chain. For lattices the checking of perfectness may be restricted to the non-comparable classes. Hence we are led to consider the following weakening of perfectness in the class of semilattices: a semilattice \(S=<S;.>\) is weakly perfect if it satisfies the condition (i') \(\forall \theta \in Con(S)\), \(x\theta a_ 1a_ 2\) with \([a_ 1]\theta\) and \([a_ 2]\theta\) non-comparable\(\to \exists x_ 1,x_ 2\in S:\) \(x_ 1\theta a_ 1\), \(x_ 2\theta a_ 2\) and \(x_ 1x_ 2=x\). With this new definition all the results of Section 1 remain true.