scholarly journals Priestley's Duality from Stone's

2000 ◽  
Vol 25 (3) ◽  
pp. 233-238 ◽  
Author(s):  
Isidore Fleisher
Keyword(s):  
Priestley's Duality

scholarly journals Distributive Ockham algebras: free algebras and injectivity

1981 ◽  
Vol 24 (2) ◽  
pp. 161-203 ◽  
Author(s):  
Moshe S. Goldberg
Keyword(s):  
Distributive Lattices ◽  
Free Algebras ◽  
Subdirectly Irreducible ◽  
Irreducible Algebra ◽  
Subdirectly Irreducible Algebra ◽  
Ockham Algebras ◽  
Subdirectly Irreducibles ◽  
Priestley's Duality

This paper centres around the variety 0 of distributive Ockham algebras, and those subvarieties of 0 which are generated by a single finite subdirectly irreducible algebra A. We use H.A. Priestley's duality for bounded distributive lattices throughout. First, intrinsic descriptions of the duals of certain finite subdirectly irreducibles are given; these are later used to determine projectives in the dual categories. Next, left adjoints to the forgetful functors from 0 and Var(A) into bounded distributive lattices are obtained, thereby allowing us to describe all free algebras and coproducts of arbitrary algebras. Finally, by applying the duality, we characterize injectivity in Var(A) for each finite subdirectly irreducible algebra A.

scholarly journals Principal congruences on distributive double p-algebras

1996 ◽  
Vol 39 (3) ◽  
pp. 491-503 ◽  
Author(s):  
Júlia Vaz De Carvalho
Keyword(s):  
Dual Space ◽  
Priestley's Duality

We use Priestley's duality to characterize, via their dual space, the distributive double p-algebras on which all congruences are principal.

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