FAQ

Reports on Mathematical Logic

logo of Jagiellonian University in Krakow

On homomorphic images and the free distributive lattice extension of a distributive nearlattice

Publication date: 14.09.2016

Reports on Mathematical Logic, 2016, Number 51, pp. 57 - 73

https://doi.org/10.4467/20842589RM.16.005.5282

Authors

,
Sergio A. Celani
CONICET and Escuela de Ciencia y Tecnologica, Universidad de San Marteen, Campus Miguelete (CP1650). San Martn, Provincia de Buenos Aires, Argentina
All publications →
Ismael Calomino
CONICET and Departamento de Matematicas, Facultad de Ciencias Exactas, Univ. Nac. del Centro, Pinto 399, 7000 Tandil, Argentina
All publications →

Abstract

In this paper we will introduce N-Vietoris families and prove that homomorphic images of distributive nearlattices are dually characterized by N-Vietoris families. We also show a topological approach of the existence of the free distributive lattice extension of a distributive nearlattice.

References

[1] J. C. Abbott, Semi-boolean algebra, Mat. Vestnik 4 (1967), 177–198.

[2] J. Arau´jo and M. Kinyon, Independent axiom systems for nearlattices, Czechoslovak Mathematical Journal 61 (2011), 975–992.

[3] G. Bezhanishvili and R. Jansana, Priestley style duality for distributive meetsemilattices, Studia Logica 98 (2011), 83–122.

[4] G. Bezhanishvili and R. Jansana, Generalized Priestley quasi-orders, Order 28 (2011), 201–220.

[5] I. Calomino and S. Celani, A note on annihilators in distributive nearlattices, Miskolc Mathematical Notes 16 (2015), 65–78.

[6] S. Celani, Topological representation of distributive semilattices, Scientiae Math. Japonicae 8 (2003), 41–51.

[7] S. Celani and I. Calomino, Some remarks on distributive semilattices, Comment. Math. Univ. Carolin. 54 (2013), 407–428.

[8] S. Celani and I. Calomino, Stone style duality for distributive nearlattices, Algebra Universalis 71 (2014), 127–153.

[9] I. Chajda, R. Halaˇs, and J. Ku¨hr, Semilattice Structures, Research and Exposition in Mathematics, Heldermann Verlag 2007.

[10] I. Chajda and M. Kolaˇr´ık, Ideals, congruences and annihilators on nearlattices, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math 46 (2007), 25–33. 

[11] I. Chajda and M. Kolaˇr´ık, Nearlattices, Discrete Math. 308 (2008), 4906–4913. 

[12] W. Cornish and R. Hickman, Weakly distributive semilattices, Acta Math. Acad. Sci. Hungar. 32 (1978), 5–16. 

[13] R. Halaˇs, Subdirectly irreducible distributive nearlattices, Miskolc Mathematical Notes 7 (2006), 141–146. 

[14] R. Hickman, Join algebras, Communications in Algebra 8 (1980), 1653–1685. 

[15] P. Johnstone, Stone spaces, Cambridge University Press, 1982. [16] M. Stone, Topological representation of distributive lattices and Brouwerian logics, Casopis pest. mat. fys. 67 (1937), 1–25.

Information

Information: Reports on Mathematical Logic, 2016, pp. 57 - 73

Article type: Original research article

Titles:

English:

On homomorphic images and the free distributive lattice extension of a distributive nearlattice

Authors

CONICET and Escuela de Ciencia y Tecnologica, Universidad de San Marteen, Campus Miguelete (CP1650). San Martn, Provincia de Buenos Aires, Argentina

CONICET and Departamento de Matematicas, Facultad de Ciencias Exactas, Univ. Nac. del Centro, Pinto 399, 7000 Tandil, Argentina

Published at: 14.09.2016

Article status: Open

Licence: None

Percentage share of authors:

Sergio A. Celani (Author) - 50%
Ismael Calomino (Author) - 50%

Article corrections:

-

Publication languages:

English

View count: 2153

Number of downloads: 1147