Quasi-Boolean powers of singular semigroups (Q1902848)

For an algebra \({\mathfrak A} = \langle A, F\rangle\) with finitary operations and a complete lattice \(L\) the \(L\)-extension of \(\mathfrak A\) is defined; this is a partial algebra whose elements are certain mappings of \(A\) into \(L\). A lattice is called quasi-Boolean if every orthogonal system in it is independent (these concepts are defined in the paper). In the case when \(L\) is quasi-Boolean, the mentioned algebra has everywhere defined operations and is called the restricted \(L\)-power of the algebra \(\mathfrak A\). This concept is studied for the case when the algebra \(\mathfrak A\) is a semigroup.