... original 1981 edition of A Course in Universal Algebra has now beenLaTeXed so the authors could make the out-of-print Springer-Verlag Gradu-ate Texts in Mathematics edition available once again, ... I§4.7 a i ,a j∈Θ (a i ,a i+1) ∨···∨Θ (a j−1 ,a j);hence a i ,a j∈Θ (a 1 ,a 2)∨···∨Θ (a n−1 ,a n). In view of (a) this leads toΘ (a 1, ,a n)⊆Θ (a 1 ,a 2)∨···∨Θ (a n−1 ,a n),soΘ (a 1, ,a n)=Θ (a 1 ,a 2)∨···∨Θ (a n−1 ,a n).(d) ... Irredundant Basis TheoremRecall that finitely generated vector spaces have the property that all minimal generatingsets have the same cardinality. It is a rather rare phenomenon, though, to have a...