# List of Errors in Free Lattices

If you find any errors, we would like to know about them. Please email us at ralph@math.hawaii.edu

Page 7, line 6
Change lattice to lattices
Page 11, proof of Lemma 1.3
(Margarita Ramalho) Zorn's lemma should be invoked here. But a direct proof avoiding Choice is not difficult.
Page 8, line 28
"An element in a lattice."
Page 18, line 22
Change "are" to "exists."
Page 71, line 12
The statement about $$J(p)$$ should read: $$J(p)$$ is the smallest set such that every join cover of an element in $$J(p)$$ can be refined to one in $$J(p)$$.
Page 98, line 38
In the proof of Lemma 5.6 replace the paragraph that begins "First consider the case ...", with

First note that if $$a \sqsubseteq c$$ and $$b \sqsubseteq c$$, then, since $$c \in A(a) \cap B(b)$$, the special property of $$\sqsubseteq$$ gives $$a \sim c \sim b$$. Now consider the case when $$a \sqsubseteq b$$. If $$b \sqsubseteq c$$, then by the above remarks $$a \sim c \sim b$$. This implies $$g(a)$$ is a joinand of $$g(b)$$, and so $$g(a) \le g(b)$$. Hence we may assume $$c \sqsubset b$$, and thus by induction $$g(a) \le g(c)$$. Also $$g(c)$$ is a joinand of $$g(b)$$ and so $$g(c) \le g(b)$$ and hence $$g(a) \le g(b)$$.

Page 99, line 29
Change $$\ll$$ to $$\leq$$
Page 100, line 16
The reference to Theorem 2.14 should be to Corollary 2.16.
Page 108, Theorem 5.33
The first item should simply read: (1) $$L = D(\mathbf{L})$$.
Page 141, Corollary 6.12
Change both occurances of $$\sigma$$ to $$\tau$$ in this corollary since $$\sigma$$ is used for a certain endomorphism of FL(X) in this chapter. Also change the $$\sigma$$ on the subscript of y in line 10 to $$\tau$$ but leave the three $$\sigma$$'s in the displayed formula above alone.
Page 212, line (3) of the listing
Change P to S.
Page 217, line (7) of the listing
Remove the statement $$T\gets\emptyset$$ and place it in between lines (8) and (9) (and renumber the lines).
Page 217, line (14) of the listing
Change the $$\lt$$ to $$\gt$$.

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