A note on the weak subalgebra lattice of a unary algebra with constants (Q2754935)

Investigations of relationships between (total) algebras or varieties of algebras and their subalgebra lattices are one of the most interesting parts of universal algebra. NEWLINENEWLINENEWLINEA description of algebras or varieties of algebras, classical algebras -- Boolean algebras, groups and modules which have special subalgebra lattices (i.e. modular, distributive, etc.) -- was given by \textit{P. P. Palfy} [Algebra Univers. 27, 220-229 (1990; Zbl 0708.08002)] and \textit{E. Lukács} and \textit{P. P. Palfy} [Arch. Math. 46, 18-19 (1986; Zbl 0998.20500)]. NEWLINENEWLINENEWLINEIn the present paper the author proves the following results: Let \(A\) be a total and locally finite algebra having finitely many constants and only unary operations. Then for every partial algebra \(B\) of the same type, if the weak subalgebra lattices of \(A\) and \(B\) are isomorphic, then their strong subalgebra lattices are also isomorphic, and \(B\) is also total and locally finite.