Weak subalgebra lattices of monounary partial algebras. (English) Zbl 0711.08007

Bartol, Wiktor

Commentat. Math. Univ. Carol. 31, No. 3, 411-414 (1990).

Monounary partial algebras are determined by their weak subalgebra lattices, namely: Theorem. Let \({\mathfrak A}\) be a partial monounary algebra. Then \({\mathfrak A}\) is uniquely determined in the class of all partial monounary algebras by its weak subalgebra lattice iff each connected component of \({\mathfrak A}\) with more than two elements contains a symmetric cycle.

Reviewer: B.Wojdyło

MSC:

08A55	Partial algebras
08A60	Unary algebras
05C75	Structural characterization of families of graphs
08A30	Subalgebras, congruence relations

Keywords:

functional graph; partial algebras; weak subalgebra lattices; monounary algebra