On homomorphic images and the free distributive lattice extension of a distributive nearlattice
cytuj
pobierz pliki
RIS BIB ENDNOTEChoose format
RIS BIB ENDNOTEOn 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.16.005.5282Authors
On homomorphic images and the free distributive lattice extension of a distributive nearlattice
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.
[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: Reports on Mathematical Logic, 2016, Number 51, pp. 57-73
Article type: Original article
Titles:
On homomorphic images and the free distributive lattice extension of a distributive nearlattice
On homomorphic images and the free distributive lattice extension of a distributive nearlattice
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:
Article corrections:
-Publication languages:
EnglishView count: 2224
Number of downloads: 1192