Counting relations on Ockham algebras

Brian A. Davey; Long T. Nguyen; Jane G. Pitkethly

doi:10.1007/s00012-015-0334-3

Counting relations on Ockham algebras

Algebra Universalis ◽

10.1007/s00012-015-0334-3 ◽

2015 ◽

Vol 74 (1-2) ◽

pp. 35-63 ◽

Cited By ~ 2

Author(s):

Brian A. Davey ◽

Long T. Nguyen ◽

Jane G. Pitkethly

Keyword(s):

Ockham Algebras

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Congruences and Kernel Ideals on a Subclass of Ockham Algebras

Studia Logica ◽

10.1007/s11225-014-9589-5 ◽

2014 ◽

Vol 103 (4) ◽

pp. 713-731 ◽

Cited By ~ 2

Author(s):

Xue-Ping Wang ◽

Lei-Bo Wang

Keyword(s):

Ockham Algebras

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Some Examples of Distributive Ockham Algebras with de Morgan Skeletons

Lattices, Semigroups, and Universal Algebra ◽

10.1007/978-1-4899-2608-1_3 ◽

1990 ◽

pp. 21-28

Author(s):

T. S. Blyth

Keyword(s):

Ockham Algebras

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Balanced pseudocomplemented Ockham algebras

Algebra Universalis ◽

10.1007/s00012-007-2029-x ◽

2007 ◽

Vol 57 (3) ◽

pp. 291-302 ◽

Cited By ~ 7

Author(s):

Jie Fang ◽

Zhong-Ju Sun

Keyword(s):

Ockham Algebras

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Ockham Algebras with Additional Operators

Logic Journal of IGPL ◽

10.1093/jigpal/12.6.447 ◽

2004 ◽

Vol 12 (6) ◽

pp. 447-459

Author(s):

Aldo V. Figallo ◽

Paolo Landini ◽

Alicia Zilliani

Keyword(s):

Ockham Algebras

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Distributive Ockham algebras: free algebras and injectivity

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700007577 ◽

1981 ◽

Vol 24 (2) ◽

pp. 161-203 ◽

Cited By ~ 21

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.

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