Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
MathSciNet review: 0412063
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 06A35

Retrieve articles in all journals with MSC: 06A35

Additional Information

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

American Mathematical Society