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Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubsti-tutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvari-eties of a given variety of that type. We then apply the results obtained to the lattice(More)
We want to extend the duality to semilattices with operators (that preserve + and 0, i.e., endomor-phisms added as operations). For simplicity, let us consider semilattices with one operator: S = S, +, 0, g, as the extension to a monoid of operators is straightforward. 1. Adjoints: the finite case We begin by recalling the general theory of adjoints on(More)
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 non-trivial functions in the clone form an order ideal.
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 non-trivial functions in the clone form an order ideal.