Finitely generated free orthomodular lattices. III (Q1586468)

For all \(k\in N\), the authors give a description of finitely generated free algebras in the variety generated by the horizontal sum of one three-atomic block \(2^3\) and \(k-1\) two-atomic blocks \(2^2\). This extends the results obtained in Part I [\textit{M. Haviar, P. Konôpka, H. A. Priestley} and \textit{C. B. Wegener}, Int. J. Theor. Phys. 36, No. 12, 2639-2660 (1997; Zbl 0899.06004)] and in Part II [\textit{M. Haviar, P. Konôpka} and \textit{C. B. Wegener}, Int. J. Theor. Phys. 36, No. 12, 2661-2679 (1997; Zbl 0899.06005)] for the (smaller) variety generated by the horizontal sum of \(k\) two-atomic blocks \(2^2\) (i.e., by the modular ortholattice \(MO_k\)).