A b s t r a c t. In this paper, the structure of finitely generated free objects in the variety of three-valued closure Lukasiewicz algebras is determined. We describe their indecomposable factors and we give their cardinality.
A b s t r a c t. It is well known that the number of subalgebras of a Boolean algebra with n atoms is the number of partitions of an n-element set. In this note we characterize the subalgebras of a finite monadic Boolean algebra and we determine the cardinality of the set of such subalgebras. For a finite n-element set X, n ≥ 1, let N [X] denote the number… (More)