Residual finiteness and related properties in monounary algebras and their direct products
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In this paper we discuss the relationship between direct products of monounary algebras and their components, with respect to the properties of residual finiteness, strong/weak subalgebra separability, and complete separability. For each of these properties P, we give a criterion CP such that a monounary algebra A has property P if and only if it satisfies CP. We also show that for a direct product A×B of monounary algebras, A×B has property P if and only if one of the following is true: either both A and B have property P, or at least one of A or B are backwards-bounded, a special property which dominates direct products and which guarantees all P hold.
De Witt , B 2021 , ' Residual finiteness and related properties in monounary algebras and their direct products ' , Algebra Universalis , vol. 82 , 32 . https://doi.org/10.1007/s00012-021-00727-4
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