De Morgan algebras with a quasi-Stone operator

T. S. Blyth; Jie Fang; Lei-bo Wang

doi:10.1007/s11225-013-9538-8

De Morgan algebras with a quasi-Stone operator

T. S. Blyth^*, Jie Fang, Lei-bo Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the class of those algebras (L; A(0), *) in which (L; A(0)) is a de Morgan algebra, (L; *) is a quasi-Stone algebra, and the operations and are linked by the identity x**A(0) = x*A(0)*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.

Original language	English
Pages (from-to)	75-90
Number of pages	16
Journal	Studia Logica
Volume	103
Issue number	1
DOIs	https://doi.org/10.1007/s11225-013-9538-8
Publication status	Published - Feb 2015

Keywords

De Morgan algebra
Quasi-Stone algebra
QSM-algebra
Subdirectly irreducible

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10.1007/s11225-013-9538-8

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abstract = "We investigate the class of those algebras (L; A(0), *) in which (L; A(0)) is a de Morgan algebra, (L; *) is a quasi-Stone algebra, and the operations and are linked by the identity x**A(0) = x*A(0)*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.",

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AU - Fang, Jie

AU - Wang, Lei-bo

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N2 - We investigate the class of those algebras (L; A(0), *) in which (L; A(0)) is a de Morgan algebra, (L; *) is a quasi-Stone algebra, and the operations and are linked by the identity x**A(0) = x*A(0)*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.

AB - We investigate the class of those algebras (L; A(0), *) in which (L; A(0)) is a de Morgan algebra, (L; *) is a quasi-Stone algebra, and the operations and are linked by the identity x**A(0) = x*A(0)*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.

KW - De Morgan algebra

KW - Quasi-Stone algebra

KW - QSM-algebra

KW - Subdirectly irreducible

U2 - 10.1007/s11225-013-9538-8

DO - 10.1007/s11225-013-9538-8

M3 - Article

SN - 0039-3215

VL - 103

SP - 75

EP - 90

JO - Studia Logica

JF - Studia Logica

IS - 1

ER -

De Morgan algebras with a quasi-Stone operator

Abstract

Keywords

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