Erratum to: A classification of certain group-like FL\(_e\)-chains

The proof of Lemma 9 is wrong. Indeed, \(a=\sup (Z)\) does not imply \(\hat{A}(a)^{^\prime }=\sup ({A(z)}{^\prime })\), and thus \(a\otimes {\hat{A}(a)}{^\prime }\) is not necessarily equal to \(\sup \{z\otimes {A(z)}{^\prime }:z \in X\}\). The statement of Lemma 9 itself is false, too. Therefore, modify Theorem 4 as follows.

Theorem 4

If \({\fancyscript{U}}\) is an absorbent-continuous group-like FL\(_e\)-algebra on a complete, weakly real chain then its negative cone is a BL-algebra with components which are either cancellative or MV-algebras with two elements, and with no two consecutive cancellative components, its positive cone is the dual of its negative cone with respect to \({^\prime }\), and its monoid operation is given by (6).

Keep the first half of the proof of Theorem 4 (the one which is about the complete, weakly real case), and erase the second half (the one which is about the subreal case).