Retract varieties of monounary algebras
Danica Jakubı́ková-Studenovská · Czechoslovak Mathematical Journal · 1997
In [1] the notion of order variety was defined as follows: an order variety is a class X of ordered sets which contains all retracts of members of X and all direct products of nonempty families of members of X.Analogously to [1], a class <# of monounary algebras will be said to be a retract variety if it is closed with respect to isomorphisms and if it contains all retracts of members of X and all direct products of nonempty families of members of X'.Retracts of monounary algebras were studied in [2] and [3].We denote by £H the collection of all retract varieties of monounary algebras.This collection is considered to be partially ordered by the class-theoretical inclusion.The aim of the present paper is to investigate the properties of the partially ordered collection *R.The main results are Theorems 2.5', 2.1V and 3.10. RETRACT VARIETY GENERATED BY Jf