Optimal natural dualities
نویسندگان
چکیده
منابع مشابه
Optimal Natural Dualities. Ii: General Theory
A general theory of optimal natural dualities is presented, built on the test algebra technique introduced in an earlier paper. Given that a set R of finitary algebraic relations yields a duality on a class of algebras A = ISP(M), those subsets R′ of R which yield optimal dualities are characterised. Further, the manner in which the relations in R are constructed from those in R′ is revealed in...
متن کاملOptimal natural dualities for varieties of Heyting algebras
The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality...
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Traditionally in natural duality theory the algebras carry no topology and the objects on the dual side are structured Boolean spaces. Given a duality, one may ask when the topology can be swapped to the other side to yield a partner duality (or, better, a dual equivalence) between a category of topological algebras and a category of structures. A prototype for this procedure is provided by the...
متن کاملRegularising Natural Dualities
Given an algebra M we may adjoin an isolated zero to form an algebra M∞ satisfying all identities u ≈ v true in M for which u and v contain the same variables. Drawing on the structure theory of P lonka sums, we show that if M is a finite, dualisable algebra which is strongly irregular, then M∞ is also dualisable. Turning the construction of M∞ upside-down for the two-element left-zero band, we...
متن کاملNatural Dualities for Semilattice-based Algebras
While every finite lattice-based algebra is dualisable, the same is not true of semilattice-based algebras. We show that a finite semilattice-based algebra is dualisable if all its operations are compatible with the semilattice operation. We also give examples of infinite semilattice-based algebras that are dualisable. In contrast, we present a general condition that guarantees the inherent non...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1993
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1993-1169079-7