Abstract
A clone C is essentially minimal if it contains an essential nonidempotent operation and every proper subclone of C is essentially unary. For a finite universe we determine all essentially minimal clones generated by groupoids of a certain type by means of four varieties and a family of varieties. We narrow the essentially minimal clones generated by groupoids of another type into three families.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Csákány, B., All minimal clones on the three-element set, Ada Cybernet. 6 (1983), 227–238.
Machida, H., Essentially minimal closed sets in multiple-valued logic, Trans. IECE Japan E 64 (1981) no. 4, 243–245.
Machida, H., Toward a classification of minimal closed sets in 3-valued logics, in: Proc. 12th Internat. Symposium on Multiple-Valued Logic, Paris 1982, IEEE Computer Soc. Publ. Office, 1982, 313–317.
Machida, H., Rosenberg, I.G., Classifying essentially minimal clones, in: Proc. 14th Internat. Symposium on Multiple-Valued Logic, Winnipeg 1984, IEEE Computer Soc. Publ. Office, 1984, 4–7.
Machida, H., Rosenberg, I.G., Essentially minimal groupoids, in Proc. 15th Internat. Symposium on Multiple-Valued Logic, Kingston, Ont., May 1985, IEEE Computer Soc. Publ. Office 1985, 338–344.
Machida, H., Rosenberg, I.G., A “large” essentially minimal clone over an infinite set, Contemp. Math. 131(1992) part 3, 159–167.
Quackenbush, R.W., A survey of minimal clones, Preprint, University of Manitoba 1991, 15 pp. To appear in Aequationes Math.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Machida, H., Rosenberg, I.G. (1993). Essentially Minimal Groupoids. In: Rosenberg, I.G., Sabidussi, G. (eds) Algebras and Orders. NATO ASI Series, vol 389. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0697-1_7
Download citation
DOI: https://doi.org/10.1007/978-94-017-0697-1_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4243-9
Online ISBN: 978-94-017-0697-1
eBook Packages: Springer Book Archive