Narrow Results

We give an infinite family of finite dualizable unary algebras that are not fully κ-dualizable, for all cardinals κ.

A finite unary algebra of finite type with a constant function 0 that is a one-element subalgebra, and whose operations have range {0, 1}, is called a {0, 1}-valued unary algebra with 0. Such an algebra has a finite basis for its quasi-equations if and only if the relation defined by the rows of the nontrivial functions in the clone form an order ideal.

A finite unary algebra $(A,F)$ has only countably many countable subdirect powers if and only if every operation $f\in F$ is either a permutation or a constant mapping.

The pre-period of a finite algebra is the maximum pre-period of its endomorphisms. We know that the pre-period of any finite modular lattice is less than or equal to the length of the lattice. A finite modular lattice is said to have the maximum pre-period property (MPP) if its pre-period and its length are equal. In this paper, we study MPP of the direct product of chains.