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Dualities for equational classes of Brouwerian algebras and Heyting algebras


Author: Brian A. Davey
Journal: Trans. Amer. Math. Soc. 221 (1976), 119-146
MSC: Primary 06A35
DOI: https://doi.org/10.1090/S0002-9947-1976-0412063-9
MathSciNet review: 0412063
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Abstract: This paper focuses on the equational class $ {{\mathbf{S}}_n}$ of Brouwerian algebras and the equational class $ {{\mathbf{L}}_n}$ of Heyting algebras generated by an n-element chain. Firstly, duality theories are developed for these classes. Next, the projectives in the dual categories are determined, and then, by applying the dualities, the injectives and absolute subretracts in $ {{\mathbf{S}}_n}$ and $ {{\mathbf{L}}_n}$ are characterized. Finally, free products and the finitely generated free algebras in $ {{\mathbf{S}}_n}$ and $ {{\mathbf{L}}_n}$ are described.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0412063-9
Keywords: Distributive lattice, Brouwerian algebra, Heyting algebra, relative Stone algebra, L-algebra, Boolean space, duality, projective, injective, weak injective, absolute subretract, free product, free algebra
Article copyright: © Copyright 1976 American Mathematical Society

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