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

• Autorzy: Celani S. , Calomino I.

Identyfikatory

DOI

10.4467/20842589RM.16.005.5282

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

distributive nearlattice; prime ideal; homomorphic image

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2016
• Tom: Vol. 51
• Strony: 57--73
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Celani S.

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

autor

Calomino I.

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

Bibliografia

• [1] J. C. Abbott, Semi-boolean algebra, Mat. Vestnik 4 (1967), 177-198.
• [2] J. Araűjo 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. Halaš, and J. Kühr, Semilattice Structures, Research and Exposition in Mathematics, Heldermann Verlag 2007.
• [10] I. Chajda and M. Kolařik, Ideals, congruences and annihilators on nearlattices, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math 46 (2007), 25-33.
• [11] I. Chajda and M. Kolařik, 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. Halaš, 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.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.