Abstract
In Parts III–V, we discuss a subfield of Lattice Theory that started with the following result—a converse of Theorem 3.4, the Funayama -Nakayama result, [53].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
K. P. Bogart , R. Freese , and J. P. S. Kung (editors), The Dilworth Theorems. Selected papers of Robert P. Dilworth, Birkhäuser Boston, Inc., Boston, MA, 1990. xxvi+465 pp. ISBN: 0-8176-3434-7
P. Crawley and R. P. Dilworth , Algebraic Theory of Lattices. Prentice-Hall, Englewood Cliffs, NJ, 1973. vi+201 pp. ISBN: 0-13-022269-0
N. Funayama and T. Nakayama , On the congruence relations on lattices, Proc. Imp. Acad. Tokyo 18 (1942), 530–531.
G. Grätzer, General Lattice Theory, second edition, new appendices by the author with B. A. Davey , R. Freese , B. Ganter , M. Greferath , P. Jipsen , H. A. Priestley , H. Rose , E. T. Schmidt, S. E. E. T. Schmidt, F. Wehrung , and R. Wille . Birkhäuser Verlag, Basel, 1998. xx+663 pp. ISBN: 0-12-295750-4; ISBN: 3-7643-5239-6 Softcover edition, Birkhäuser Verlag, Basel–Boston–Berlin, 2003. ISBN: 3-7643-6996-5
G. Grätzer and H. Lakser , Extension theorems on congruences of partial lattices, Notices Amer. Math. Soc. 15 (1968), 732, 785.
_________ , Notes on sectionally complemented lattices. I. Characterizing the 1960 sectional complement. Acta Math. Hungar. 108 (2005), 115–125.
_________ , Notes on sectionally complemented lattices. II. Generalizing the 1960 sectional complement with an application to congruence restrictions. Acta Math. Hungar. 108 (2005), 251–258.
G. Grätzer, H. Lakser , and M. Roddy , Notes on sectionally complemented lattices. III. The general problem, Acta Math. Hungar. 108 (2005), 325–334.
G. Grätzer and M. Roddy , Notes on sectionally complemented lattices. IV. Manuscript.
_________ , On congruence lattices of lattices, Acta Math. Acad. Sci. Hungar. 13 (1962), 179–185.
_________ , A lattice construction and congruence-preserving extensions, Acta Math. Hungar. 66 (1995), 275–288.
_________ , The Strong Independence Theorem for automorphism groups and congruence lattices of finite lattices, Beiträge Algebra Geom. 36 (1995), 97–108.
_________ , Congruence class sizes in finite sectionally complemented lattices, Canad. Math. Bull. 47 (2004), 191–205.
M. F. Janowitz , Section semicomplemented lattices, Math. Z. 108 (1968), 63–76.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Grätzer, G. (2016). The Dilworth Theorem. In: The Congruences of a Finite Lattice. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-38798-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-38798-7_8
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-38796-3
Online ISBN: 978-3-319-38798-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)