Given a countable set A, let Equ(A) denote the lattice of equivalences of A. We prove the existence of a four-generated sublattice Q of Equ(A) such that Q contains all atoms of Equ(A). Moreover, Q can be generated by four equivalences such that two of them are comparable. Our result is a reasonable generalization of Strietz [5, 6] from the finite case to the countable one; and in spite of its essentially simpler proof it asserts more for the countable case than [2, 3].
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Chajda, I. and Czédli, G. (1996) How to generate the involution lattice of quasiorders?, Studia Sci. Math. (Budapest), to appear.
Czédli, G. (1996) Four-generated large equivalence lattices, Acta Sci. Math. (Szeged), to appear.
Czédli, G. (1996) (1+1+2)-generated equivalence lattices, in preparation.
RivalI. and StanfordM. (1992) Algebraic aspects of partition lattices, in Matroids and Applications, Cambridge Univ. Press, Cambridge, pp. 106–122.
Strietz, H. (1975) Finite partition lattices are four-generated, in Proc. Lattice Th. Conf. Ulm, pp. 257–259.
StrietzH. (1977) Über Erzeugendenmengen endlicher Partitionverbände, Studia Sci. Math. Hungarica 12, 1–17.
ZádoriZ. (1986) Generation of finite partition lattices, in Colloquia Math. Soc. J. Bolyai 43, Lectures in Universal Algebra (Proc. Conf. Szeged), (1983), North-Holland, Amsterdam, New York, pp. 573–586.
Dedicated to George Grätzer on his 60th birthday
This research was supported by the NFSR of Hungary (OTKA), grant no. T7442.
Communicated by I. Rival
About this article
Cite this article
Czédli, G. Lattice generation of small equivalences of a countable set. Order 13, 11–16 (1996). https://doi.org/10.1007/BF00383964
Mathematics Subject Classifications (1985)
- Primary 06B99
- Secondary 06C10
- equivalence lattice
- generating set